Question

Solve 3x − 8 = 8 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

Answer:

(D) 9.893

Step-by-step explanation:

Given:

The equation to solve is given as:

$3^{x-8}=8$

Since, the variable 'x' is in the exponent, we take log on both the sides.

Taking log to base 3 on both the sides, we get:

$\log_3 (3^{x-8})=\log_3 (8)$

Using logarithmic property $\log a^m=m\log a$

Therefore, the left hand side of the equation becomes;

$(x-8)\log_3 3=\log_3 8$

We know that, $\log_a a=1$

$(x-8)\times 1=\log_3 8$

$x-8=\log_3 8$

Now, using the change of base property of log $\log_b y=\frac{\log y}{\log b}$, we get:

$x-8=\frac{\log 8}{\log 3}$

Adding 8 on both sides, we get:

$x-8+8=\frac{\log 8}{\log 3}+8$

$\log 8 = 0.903, \log 3 = 0.477$

$x= \frac{0.903}{0.477}+8$

$x=1.893+8=9.893$

Hence, option D is correct.