<s>[INST] Solving $6^{50-x} = 2^{50}$ I'm being asked to solve an equation for $x$, giving the answer in the form below: $$a \log_{b} c$$
One of them is: $$6^{50-x} = 2^{50}$$
So I started by taking the $\log_6$ of both sides to give:
$$\log_{6}6^{50-x}=\log_{6}2^{50} \tag1$$
Leading to:
$$\begin{align}
50-x &=\log_{6}2^{50} \tag2 \\
50-x &=50\log_{6}2 \tag3 \\
-x &=-50+50\log_{6}2 \tag4
\end{align}$$
or finally:$$x=50-50\log_{6}2 \tag5$$
I've been given the answer of: $$x=50\log_{6}3 \tag6$$
How do I get from my answer to the correct form, or have I made a mistake along the way?
Thanks,
 [/INST] Your last line:
$x= 50 -50\log_6 2$;
$x=50-50\log_6 ((2 \cdot 3)/ 3));$
Can you finish?
Option:
$(2 \cdot 3)^{50}=2^{50}6^x ;$
$2^{50}3^{50}=2^{50}6^x;$
$6^x=3^{50};$
$x=50 \log_6 3.$
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