Question

What is the solution to the equation below? Log6 4x^2-log6x=2

Answer 1

Combine the left hand side, then write both sides as powers of 6:

$\log_64x^2-\log_6x=\log_6\dfrac{4x^2}x=2\implies6^{\log_6\frac{4x^2}x}=6^2$

$\implies\dfrac{4x^2}x=36$

$\implies x^2=9x$

$\implies x^2-9x=x(x-9)=0$

$\implies x=0,x=9$

However, for any base $b$, $\log_bx$ is undefined if $x=0$, so the only solution is $x=9$.

Answer 2

Answer:

D. x=9

Step-by-step explanation: