Question

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

Answer 1

6.292

Explanation:

I got it right on the test.

Answer 2

`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`