Question

Which logarithmic equation has the same solution as x minus 4 = 2 cubed

Answer 1

Given:

The given equation is $x-4=2^{3}$

Solving the equation $x-4=2^{3}$, we get;

$x-4=8$

     $x=12$

We need to determine the logarithmic equation that is equivalent to the given equation.

Option A: $\log 3^{2}=(x-4)$

Simplifying, we get;

     $\log 9=x-4$

$\log 9+4=x$

      $4.95=x$

Since, the values of x are not equivalent, the equation $\log 3^{2}=(x-4)$ is not equivalent to $x-4=2^{3}$

Option A is not the correct answer.

Option B: $\log 2^{3}=x-4$

Simplifying, we get;

     $\log 8=x-4$

$\log 8+4=x$

        $4.9=x$

Since, the values of x are not equivalent, the equation $\log 2^{3}=x-4$ is not equivalent to $x-4=2^{3}$

Option B is not the correct answer.

Option C: $\log _{2}(x-4)=3$

Simplifying, we get;

$x-4=2^{3}$

$x-4=8$

     $x=12$

Since, the values of x are equivalent, the equation $\log _{2}(x-4)=3$ is equivalent to $x-4=2^{3}$

Hence, Option C is the correct answer.

Option D: $\log _{3}(x-4)=2$

Simplifying, we get;

$x-4=3^2$

$x-4=9$

     $x=13$

Since, the values of x are not equivalent, the equation $\log _{3}(x-4)=2$ is not equivalent to $x-4=2^{3}$

Hence, Option D is not the correct answer.

Answer 2

Answer: C

C)   log Subscript 2 Baseline (x minus 4) = 3