Math - Logarithms | Practice Hub

Simplify the expression using logarithmic identities.

$log_4(\frac{7}{5})$

$log_4(\frac{5}{7})$

The expression cannot be simplified

Explanation

The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

$log_A(\frac{B}{C})=log_AB-log_AC$

If we encounter two logarithms with the same base, we can likely combine them. In this case, we can use the reverse of the above identity.

$log_AB-log_AC=log_A(\frac{B}{C})$

$A=4,\ B=7,\ C=5$

$log_47-log_45=log_4(\frac{7}{5})$

Simplify the expression using logarithmic identities.

$log_4(\frac{7}{5})$

$log_4(\frac{5}{7})$

The expression cannot be simplified

Explanation

The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

$log_A(\frac{B}{C})=log_AB-log_AC$

If we encounter two logarithms with the same base, we can likely combine them. In this case, we can use the reverse of the above identity.

$log_AB-log_AC=log_A(\frac{B}{C})$

$A=4,\ B=7,\ C=5$

$log_47-log_45=log_4(\frac{7}{5})$

Simplify the expression using logarithmic identities.

$log_4(\frac{7}{5})$

$log_4(\frac{5}{7})$

The expression cannot be simplified

Explanation

The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

$log_A(\frac{B}{C})=log_AB-log_AC$

If we encounter two logarithms with the same base, we can likely combine them. In this case, we can use the reverse of the above identity.

$log_AB-log_AC=log_A(\frac{B}{C})$

$A=4,\ B=7,\ C=5$

$log_47-log_45=log_4(\frac{7}{5})$

Based on the definition of logarithms, what is ${\log_{10}1000}$ ?

100

Explanation

For any equation $\log_{10}(y) = x$ , $10^{x } = y$ . Thus, we are trying to determine what power of 10 is 1000. , so our answer is 3.

Based on the definition of logarithms, what is ${\log_{10}1000}$ ?

100

Explanation

For any equation $\log_{10}(y) = x$ , $10^{x } = y$ . Thus, we are trying to determine what power of 10 is 1000. , so our answer is 3.

Based on the definition of logarithms, what is ${\log_{10}1000}$ ?

100

Explanation

For any equation $\log_{10}(y) = x$ , $10^{x } = y$ . Thus, we are trying to determine what power of 10 is 1000. , so our answer is 3.

What is the value of that satisfies the equation $\log_x128=7$ ?

$\frac{1}{2}$

Explanation

$\log_xa=b$ is equivalent to . In this case, you know the value of (the argument of a logarithmic equation) and b (the answer to the logarithmic equation). You must find a solution for the base.

$x^{7}=128$

$\sqrt[7]{x}=\sqrt[7]{128}$

What is the value of that satisfies the equation $\log_x128=7$ ?

$\frac{1}{2}$

Explanation

$\log_xa=b$ is equivalent to . In this case, you know the value of (the argument of a logarithmic equation) and b (the answer to the logarithmic equation). You must find a solution for the base.

$x^{7}=128$

$\sqrt[7]{x}=\sqrt[7]{128}$

What is the value of that satisfies the equation $\log_x128=7$ ?

$\frac{1}{2}$

Explanation

$\log_xa=b$ is equivalent to . In this case, you know the value of (the argument of a logarithmic equation) and b (the answer to the logarithmic equation). You must find a solution for the base.

$x^{7}=128$

$\sqrt[7]{x}=\sqrt[7]{128}$

$\log_7118=?$

Explanation

Most of us don't know what the exponent would be if and unfortunately there is no $\log_7$ on a graphing calculator -- only $\log$ (which stands for $\log_{10}$ ).