Question

Solve. Show your work.log6(2x – 4) + 11 = 13

Answer 1

ANSWER

x = 20

EXPLANATION

To solve this equation, first, we have to subtract 11 from both sides,

$\begin{gathered} \log_6(2x-4)+11-11=13-11 \\ \\ \log_6(2x-4)=2 \end{gathered}$

Then, there is the property of logarithms that states that if we raise the base of a logarithmic expression to the expression, the result is the argument of the logarithm,

$a^{\log_a(b)}=b$

So, the next step is to raise 6 to each side of the equation,

$\begin{gathered} 6^{\log_6(2x-4)}=6^2 \\ 2x-4=36 \end{gathered}$

Then, add 4 to both sides,

$\begin{gathered} 2x-4+4=36+4 \\ 2x=40 \end{gathered}$

And divide both sides by 2,

$\begin{gathered} \frac{2x}{2}=\frac{40}{2} \\ \\ x=20 \end{gathered}$

Hence, the solution is x = 20.