Question

Given the exponential equation 3x = 27, what is the logarithmic form of the equation in base 10?

A. x = log base 10 of 3, all over log base 10 of 27
B. x = log base 10 of 27, all over log base 10 of 3
C. x = log base 2 of 3, all over log base 2 of 27
D. x = log base 2 of 10, all over log base 2 of 3

Answer 1

the correct answer is letter B or the second option

Answer 2

The exponential equation is in form of x= log base 10 of 27, all over log base 10 of 3

`x=(\log_(10)27)/(\log_(10)3)`

B is correct

Explanation:

Given: Exponential equation 3ˣ = 27

We need to write in logarithmic form with base 10

`3^x=27`

First we will apply log both sides with base 10

`\log_(10)3^x=\log_(10)27`

`x\log_(10)3=\log_(10)27`
`\because \log a^m=m\log a`

Now, we will divide by
`\log_(10)3` both sides

`x=(\log_(10)27)/(\log_(10)3)`

Hence, The exponential equation is in form of x= log base 10 of 27, all over log base 10 of 3