Question

Explain how to solve 3x − 4 = 6 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

Answer:

.5 or 1

Step-by-step explanation:

Subtract 3 on both sides.

4 = 9

and now you will divide by 4

4/4. 9/9 = 0.444444.......

and it will equal to .5 or 1

Answer 2

Answer:

$x \approx 2$

Step-by-step explanation:

The given equation is

$3^{x}-4=6$

First, we move all constant terms to one side

$3^{x}=6+4\\ 3^{x}=10$

Observe that the bases are different, so first, we rewrite the expression as logarithm

$x=log_{3}(10)$

But, we need a logarithm with base 10, so we apply the following property

$log_{a}(b)=\frac{log(b)}{log(a)}$

$x=\frac{log(10)}{log(3)}$

But, $log(10)=1$

So,

$x=\frac{1}{log(3)} \approx \frac{1}{0.50} \approx 2$