Evaluate the log without a calculator ( show your work )

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

4

Step-by-step explanation:

Given in the question a logarithm expression

We will use Exponent of Log Rule

here b = 7

        k = 16

So suppose

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 = 4

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.