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

4

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