Answer:
(D) 9.893
Step-by-step explanation:
Given:
The equation to solve is given as:
[tex]3^{x-8}=8[/tex]
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:
[tex]\log_3 (3^{x-8})=\log_3 (8)[/tex]
Using logarithmic property [tex]\log a^m=m\log a[/tex]
Therefore, the left hand side of the equation becomes;
[tex](x-8)\log_3 3=\log_3 8[/tex]
We know that, [tex]\log_a a=1[/tex]
[tex](x-8)\times 1=\log_3 8[/tex]
[tex]x-8=\log_3 8[/tex]
Now, using the change of base property of log [tex]\log_b y=\frac{\log y}{\log b}[/tex], we get:
[tex]x-8=\frac{\log 8}{\log 3}[/tex]
Adding 8 on both sides, we get:
[tex]x-8+8=\frac{\log 8}{\log 3}+8[/tex]
[tex]\log 8 = 0.903, \log 3 = 0.477[/tex]
[tex]x= \frac{0.903}{0.477}+8[/tex]
[tex]x=1.893+8=9.893[/tex]
Hence, option D is correct.
