How do you solve $36^{x + 2} = 6^{4 x}$ $36^ (x + 2) = 6 ^(4x)$ ?

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Answer 1 · 2016-04-05T05:19:59

$x = 2$ $x=2$

$1$ $1$ . Knowing that $36 = 6^{2}$ $36=6^2$ , simplify $36^{x + 2}$ $36^(x+2)$ .

$36^{x + 2} = 6^{4 x}$ $36^(x+2)=6^(4x)$

$6^{2 (x + 2)} = 6^{4 x}$ $6^(2(x+2))=6^(4x)$

$6^{2 x + 4} = 6^{4 x}$ $6^(2x+4)=6^(4x)$

$2$ $2$ . Since the powers both have the same base on either side of the equation, the exponents are equal to each other.

$2 x + 4 = 4 x$ $2x+4=4x$

$3$ $3$ . Solve for $x$ $x$ .

$2 x = 4$ $2x=4$

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How do you solve 36^ (x + 2) = 6 ^(4x) 36x+2=64x36^ (x + 2) = 6 ^(4x) ?