Logarithmic Functions - College Algebra

To solve, you must first "undo" the log. Since no base is specified, you assume it is 10. Thus, we need to take 10 to both sides.

Now, simply solve for x.

To solve, you must combine the logs into 1 log, instead of three separate ones. To do this, you must remember that when adding logs, you multiply their insides, and when you subtract them, you add their insides. Therefore,

To solve this natural logarithm equation, we must eliminate the operation. To do that, we must remember that is simply with base . So, we raise both side of the equation to the power.

This simplifies to

. Remember that anything raised to the 0 power is 1.

Continuing to solve for x,

To eliminate the operation, simply raise both side of the equation to the power because the base of the operation is 7.

This simplifies to

is a direct statement of the Change of Base Property of Logarithms. If and , this property holds true for any - not just .

is undefined for two reasons: first, the base of a logarithm cannot be negative, and second, a negative number cannot have a logarithm.

, so

, so the above becomes

By the Change of Base Property,

, so the above becomes

,

the correct response.

, so

, so the above becomes

, so the above becomes

We expand this logarithm based on the property:

and .

We expand this logarithm based on the following properties:

We condense this logarithm based on the following properties:

To solve, you must first "undo" the log. Since no base is specified, you assume it is 10. Thus, we need to take 10 to both sides.

Now, simply solve for x.

To solve, you must combine the logs into 1 log, instead of three separate ones. To do this, you must remember that when adding logs, you multiply their insides, and when you subtract them, you add their insides. Therefore,

To solve for y we first need to get rid of the logs.

Then we get .

After that, we simply have to divide by 5x on both sides:

To solve this natural logarithm equation, we must eliminate the operation. To do that, we must remember that is simply with base . So, we raise both side of the equation to the power.

This simplifies to

. Remember that anything raised to the 0 power is 1.

Continuing to solve for x,

To eliminate the operation, simply raise both side of the equation to the power because the base of the operation is 7.

This simplifies to

is a direct statement of the Change of Base Property of Logarithms. If and , this property holds true for any - not just .

is undefined for two reasons: first, the base of a logarithm cannot be negative, and second, a negative number cannot have a logarithm.

, so

, so the above becomes

By the Change of Base Property,

, so the above becomes

,

the correct response.