Question
Solve for $x : 2^{5x-1}= 42^{3x + 1}$
✓
Answer
$2^{5 x-1}=4 \times 2^{3 x+1}$
$ \Rightarrow 2^{5 x-1}=2^2 \times 2^{3 x+1}$
$ \Rightarrow 2^{5 x-1}=2^{2+3 x+1}$
$ \Rightarrow 2^{5 x-1}=2^{3 x+3}$
We know that if bases are equal, the powers are equal
$\Rightarrow 5 x-1=3 x+3$
$ \Rightarrow 5 x-3 x=3+1$
$ \Rightarrow 2 x=4$
$ \Rightarrow x=\frac{4}{2}$
$ \Rightarrow x=2 .$
$ \Rightarrow 2^{5 x-1}=2^2 \times 2^{3 x+1}$
$ \Rightarrow 2^{5 x-1}=2^{2+3 x+1}$
$ \Rightarrow 2^{5 x-1}=2^{3 x+3}$
We know that if bases are equal, the powers are equal
$\Rightarrow 5 x-1=3 x+3$
$ \Rightarrow 5 x-3 x=3+1$
$ \Rightarrow 2 x=4$
$ \Rightarrow x=\frac{4}{2}$
$ \Rightarrow x=2 .$
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