algebra 2 log i need help

Question

what is log5x=2 in exponential for?

Answer 1

In order to solve this, you need to use the defining relationship between logarithms and exponents!

By definition, log_b(x) = y is true when b^y = x, where b is the base of the log and x is the argument. In words, raising b to the y will give us x.

Applying this to your problem we have log₅x = 2! So we know here that 5 will be b, x will be x, and y will be 2.

Using the formula above, we know that to convert this to the exponential form, we will raise 5 to the 2 to give us x! Writing this out, we have

5² =x, which is the log in exponential form!

To solve it, you simplify

25 = x

Answer 2

If the base is not written, you assume it is base 10.

To go from Log form to exponential form, follow this rule:

Log (base b) A=X to b^X=A

So for this one: log (base10)5x=2 you would write 10^2=5x

If you need to solve more, 100=5x after squaring the 10

Divide both sides by 5: 20=x

Answer 3

I'm assuming log() here is the base 10 log, log₁₀(), and not the natural log, ln().

Taking both sides of the equation to the power of 10.

10^log(5x) = 10² = 100

The question looks like it was cut off in the middle. I'm guessing you need to solve for x

Log rule, a^log_a^(b) = b

5x = 100

x= 20