Answer:
Value of x is 6.
Step-by-step explanation:
Using logarithmic rules:
- \(\log_b mn = \log_b m+ \log_b n\)
- \(\log_b x^n = n \log_b\)
- if \(\log_b x = \log_b y\) then x = y
Solve: \(4 \log_{12} 2+\log_{12} x = \log_{12} 96\)
Apply the logarithmic rules:
\(\log_{12} 2^4+\log_{12} x = \log_{12} 96\)
\(\log_{12} 16+\log_{12} x = \log_{12} 96\)
then;
\(\log_{12} 16x = \log_{12} 96\)
Again apply the same rules:
16x = 96
Divide both sides by 6 we get;
x = 6
therefore, the value of x is 6
