How to find an exponent from a rational number - PSAT Math

Card 1 of 70

Didn't Know

Knew It

1 of 2019 left

Question

Which of the following lists the above quantities from least to greatest?

Tap to reveal answer

Answer

← Didn't Know|Knew It →

Question

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

Tap to reveal answer

Answer

The answer is 33 = 27

← Didn't Know|Knew It →

Question

Solve for .

$2^{x}$= 64

Tap to reveal answer

Answer

Since $2^{x}$= $2^{6}$

Hence

← Didn't Know|Knew It →

Question

Simplify:

Tap to reveal answer

Answer

← Didn't Know|Knew It →

Question

Solve for :

$$\sqrt{x}$ -1= 4$

Tap to reveal answer

Answer

From the equation one can see that

$$\sqrt{x}$ = 5$

Hence must be equal to 25.

← Didn't Know|Knew It →

Question

Evaluate:

$\log 0.1=$

Tap to reveal answer

Answer

$0.1= $10^{-1}$$

$\log 0.1=-1$

← Didn't Know|Knew It →

Question

Solve for .

Tap to reveal answer

Answer

$x= $2^4${}= 16$

← Didn't Know|Knew It →

Question

Solve for .

$\log _{9}x=\frac{1}{2}$$

Tap to reveal answer

Answer

$\log _{9}x=\frac{1}{2}$$

$x = $9^{$\frac{1}${2}$}= 3$

← Didn't Know|Knew It →

Question

Solve for .

$\log (x+3)+\log x=1$

Tap to reveal answer

Answer

Use the rules of logarithms to combine terms.

$\log (x(x+3))=1$

Hence,

By fatoring we get

Hence $x=-5\ or\ 2$ .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

← Didn't Know|Knew It →

Question

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

Tap to reveal answer

Answer

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is .

← Didn't Know|Knew It →

Question

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

Tap to reveal answer

Answer

The answer is 33 = 27

← Didn't Know|Knew It →

Question

Which of the following lists the above quantities from least to greatest?

Tap to reveal answer

Answer

← Didn't Know|Knew It →

Question

Solve for .

$2^{x}$= 64

Tap to reveal answer

Answer

Since $2^{x}$= $2^{6}$

Hence

← Didn't Know|Knew It →

Question

Simplify:

Tap to reveal answer

Answer

← Didn't Know|Knew It →

Question

Solve for :

$$\sqrt{x}$ -1= 4$

Tap to reveal answer

Answer

From the equation one can see that

$$\sqrt{x}$ = 5$

Hence must be equal to 25.

← Didn't Know|Knew It →

Question

Evaluate:

$\log 0.1=$

Tap to reveal answer

Answer

$0.1= $10^{-1}$$

$\log 0.1=-1$

← Didn't Know|Knew It →

Question

Solve for .

Tap to reveal answer

Answer

$x= $2^4${}= 16$

← Didn't Know|Knew It →

Question

Solve for .

$\log _{9}x=\frac{1}{2}$$

Tap to reveal answer

Answer

$\log _{9}x=\frac{1}{2}$$

$x = $9^{$\frac{1}${2}$}= 3$

← Didn't Know|Knew It →

Question

Solve for .

$\log (x+3)+\log x=1$

Tap to reveal answer

Answer

Use the rules of logarithms to combine terms.

$\log (x(x+3))=1$

Hence,

By fatoring we get

Hence $x=-5\ or\ 2$ .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

← Didn't Know|Knew It →

Question

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

Tap to reveal answer

Answer

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is .

← Didn't Know|Knew It →

Knew It

How to find an exponent from a rational number - PSAT Math

Which of the following lists the above quantities from least to greatest?

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

The answer is 33 = 27

Solve for . $2^{x}$= 64

Since $2^{x}$= $2^{6}$ Hence

Simplify:

Solve for :

From the equation one can see that Hence must be equal to 25.

Evaluate:

Solve for .

Solve for .

Solve for .

Use the rules of logarithms to combine terms. Hence, By fatoring we get Hence . However, you cannot take the logarithm of a negative number. Thus, the only value for is .

and Find

Hence the correct answer is .

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

The answer is 33 = 27

Which of the following lists the above quantities from least to greatest?

Solve for . $2^{x}$= 64

Since $2^{x}$= $2^{6}$ Hence

Simplify:

Solve for :

From the equation one can see that Hence must be equal to 25.

Evaluate:

Solve for .

Solve for .

Solve for .

Use the rules of logarithms to combine terms. Hence, By fatoring we get Hence . However, you cannot take the logarithm of a negative number. Thus, the only value for is .

and Find

Hence the correct answer is .

Solve for .

$2^{x}$= 64

Since $2^{x}$= $2^{6}$

Hence

Solve for :

$$\sqrt{x}$ -1= 4$

From the equation one can see that

$$\sqrt{x}$ = 5$

Hence must be equal to 25.

Evaluate:

$\log 0.1=$

Solve for .

$\log _{9}x=\frac{1}{2}$$

Solve for .

$\log (x+3)+\log x=1$

Use the rules of logarithms to combine terms.

$\log (x(x+3))=1$

Hence,

By fatoring we get

Hence $x=-5\ or\ 2$ .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is .

Solve for .

$2^{x}$= 64

Since $2^{x}$= $2^{6}$

Hence

Solve for :

$$\sqrt{x}$ -1= 4$

From the equation one can see that

$$\sqrt{x}$ = 5$

Hence must be equal to 25.

Evaluate:

$\log 0.1=$

Solve for .

$\log _{9}x=\frac{1}{2}$$

Solve for .

$\log (x+3)+\log x=1$

Use the rules of logarithms to combine terms.

$\log (x(x+3))=1$

Hence,

By fatoring we get

Hence $x=-5\ or\ 2$ .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is .