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

Value of x is 6.

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

Answer 2

`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 )