Answer:
3
The Problem:
[tex]\log_{x-1}(16)=4[/tex].
Step-by-step explanation:
Based on your choices I think you mean:
[tex]\log_{x-1}(16)=4[/tex].
The equivalent exponential form is:
[tex](x-1)^4=16[/tex]
Take the fourth of both sides:
[tex](x-1)=\pm 16^\frac{1}{4}[/tex]
( There is two answer because it was even powered.)
Simplify:
[tex]x-1=\pm 2[/tex]
Add 1 on both sides.
[tex]x=1+2=3 \text{ or } x=1-2=-1[/tex]
Since the base of logarithm can only be postive not including 1, then the answer is just x=3. As x=-1 gives the base as x-1=-1-1=-2.
