Question

Evaluate the log without a calculator ( Show your work )

The problem is in the image. I don't know how to write it.

Answer 1

Answer:

4

Step-by-step explanation:

Given in the question a logarithm expression

$7^(log_{49}16 )$

We will use Exponent of Log Rule

$b^(log_{b}k ) = k$

here b = 7

        k = 16

So suppose

$7^(log_{49}16 ) = x\\Take square on both sides\\(7^(log_{49}16 ) )^{2} = x^2\\49^(log_{49}16)= x^2$

Now, according to the rule

16 = x²

to find x only take square root on both sides of the equation

x = √16

x = 4

so $7^(log_{49}16 )$ = 4