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Algebra Difficulty 2.3 Junior Find the answer

The number of real values of xx that satisfy the equation (26x+3)(43x+6)=84x+5(2^{6x+3})(4^{3x+6})=8^{4x+5} is:
$\text{

Pick one

Solution

We know that
26x+3⋅43x+6=26x+3⋅(22)3x+6=26x+3⋅26x+12=212x+152^{6x+3}\cdot4^{3x+6}=2^{6x+3}\cdot(2^2)^{3x+6}=2^{6x+3}\cdot2^{6x+12}=2^{12x+15}.
We also know that
84x+5=(23)4x+5=212x+158^{4x+5}=(2^3)^{4x+5}=2^{12x+15}.
There are infinite solutions to the equation 212x+15=212x+152^{12x+15}=2^{12x+15}, so the answer is (E) greater than 3\boxed{\text{(E) greater than 3}}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.