Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b

Question

asked Mar 24, 2020 208k views

2 Answers

Ryan Morton · Answer 1 · 2020-03-27T20:53:23+0000

Answer:

4^x-5=6 gives the solution
$x=(\log(11))/(\log(4))$ .

4^(x-5)=6 gives the solution
$x=(\log(6))/(\log(4))+5$ .

Explanation:

I will solve both interpretations.

If we assume the equation is
4^(x)-5=6 , then the following is the process:

4^x-5=6

Add 5 on both sides:

4^x=6+5

Simplify:

4^x=11

Now write an equivalent logarithm form:

$\log_4(11)=x$

$x=\log_4(11)$

Now using the change of base:

$x=(\log(11))/(\log(4))$ .

If we assume the equation is
4^(x-5)=6 , then we use the following process:

4^(x-5)=6

Write an equivalent logarithm form:

$\log_4(6)=x-5$

$x-5=\log_4(6)$

Add 5 on both sides:

$x=\log_4(6)+5$

Use change of base formula:

$x=(\log(6))/(\log(4))+5$