Question

Solve 4 log12 2 + log12 x = log12 96. Choose one answer.. a. x = 88. b. x = 80. c. x = 12. d. x = 6

Answer 1

D is the correct answer for the given equation.

Answer 2

Option (d) is correct.

The solution of x for the given equation
`4log_(12)2\:+\:log_(12)x=log_(12)96` is 6.

Explanation:

Given :
`4log_(12)2\:+\:log_(12)x=log_(12)96`

We have to solve for x.

Consider the given equation
`4log_(12)2\:+\:log_(12)x=log_(12)96`

Subtract
`4\log _(12)\left(2\right)` both side, we have,

`4\log _(12)\left(2\right)+\log _(12)\left(x\right)-4\log _(12)\left(2\right)=\log _(12)\left(96\right)-4\log _(12)\left(2\right)`

Simplify, we have,

`\log _(12)\left(x\right)=\log _(12)\left(96\right)-4\log _(12)\left(2\right)`

Consider Right side of above,

`\log _(12)\left(96\right)-4\log _(12)\left(2\right)`

Apply log rule,
`\:a\log _c\left(b\right)=\log _c\left(b^a\right)`

`4\log _(12)\left(2\right)=\log _(12)\left(2^4\right)`

`=\log _(12)\left(96\right)-\log _(12)\left(2^4\right)`

Again applying log rule,
`\log _c\left(a\right)-\log _c\left(b\right)=\log _c\left((a)/(b)\right)`

`\log _(12)\left(96\right)-\log _(12)\left(2^4\right)=\log _(12)\left((96)/(2^4)\right)`

Simplify, we have,

`=\log _(12)\left(6\right)`

`\log _(12)\left(x\right)=\log _(12)\left(6\right)`

when log have same base,

`\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)`

Thus, x = 6

Thus, The solution of x for the given equation
`4log_(12)2\:+\:log_(12)x=log_(12)96` is 6.