Question

What is the solution of log base of (3x-7) 25=2?

a. x=-2
b. x=2
c. x=3
d. x=4

Answer 1

d. x=4

Explanation:

So we have the following equation:
`log_((3x-7))25=2`

Now to understand how we can rewrite this equation, let's go over the definition of a log:
`log_ba=x\implies b^x=a`

So this value of "log base b of a" Is equal to the value that I have to raise the base b to, to get the result a

So when I have the equation:
`log_((3x-7))25=2`

This is essentially saying, I have to raise (3x-7) the base, to the power of 2, to get the result of 25

So let's rewrite it using the definition of a log

`(3x-7)^2=25`

Take the square root of both sides

`3x-7=5`

add 7 to both sides

`3x=7+5`

Now divide both sides by 3

`x=(7\pm5)/(3)`

Simplifying:

`x=4`