Question

Write the equation in logarithmic form.

2^5 = 32

A. log32 = 5 • 2

B. log232 = 5

C. log32 = 5

D. log532 = 2

Answer 1

The answer is C.
`log_2(32)=5`

Explanation:

The logarithmic form is:

`log_b(x)=y\\b^y=x\\`

Where:

b is the base of the logarithmic.

In this case, the base could be "2" because the left side of the equation has a 2 powered by 5 and the right side of the equation has a 32 that is equal to 2 powered by 6. Also we can apply the next property:

`log(a^b)=b*log(a)`

So, we have to reverse the form from exponential to logarithmic.

Then:

`2^5=32\\log_2(2^5)=log_2(32)\\5*log_2(2)=log_2(32)\\5*1=log_2(32)\\log_2(32)=5`

Finally, the equation in logarithmic form is C.
`log_2(32)=5`

Answer 2

An equation with the form
`b^x=y` has a logarithmic form of
`log_b(y) = x.`. The logarithmic form of
`2^5=32` where in b = 2, x=5, and y=32 is

`log_232=5`.