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

Answer:

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

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

Step-by-step 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:

$x=\frac{\log(11)}{\log(4)}$.

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:

$x=\frac{\log(6)}{\log(4)}+5$