Question

Solve logx − 1 16 = 4. a) x = 2 b)x = 3 c)x = 4 d)x = 5

Answer 1

Answer:

3

The Problem:

$\log_{x-1}(16)=4$.

Step-by-step explanation:

Based on your choices I think you mean:

$\log_{x-1}(16)=4$.

The equivalent exponential form is:

$(x-1)^4=16$

Take the fourth of both sides:

$(x-1)=\pm 16^\frac{1}{4}$

( There is two answer because it was even powered.)

Simplify:

$x-1=\pm 2$

Add 1 on both sides.

$x=1+2=3 \text{ or } x=1-2=-1$

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.