Question

Solve 4 log12 2 + log12 x = log12 96. Choose one answer.. a. x = 88. b. x = 80. c. x = 12. d. x = 7

Answer 1

$4log_{12} 2 + log_{12} x = log_{12} 96 \\ log _{12} 2^{4} +log _{12} x = log _{12} 96 \\ log _{12} 16x = log_{12} 96$
16 x = 96
x = 96 : 16 = 6
Answer : D ) x = 6 ( x = 7 is the wrong answer ) 

Answer 2

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