What is the solution set of $4 [9^{x - 1}] = 108$ $4[9^(x-1)] = 108$ ?

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What is the solution set of $4 [9^{x - 1}] = 108$ $4[9^(x-1)] = 108$ ?

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Answer 1 · 2015-05-10T21:32:18

Take 4 to the right:
$9^{x - 1} = \frac{108}{4} = 27$ $9^(x-1)=108/4=27$
$9^{x - 1} = 3^{3}$ $9^(x-1)=3^3$
But $9 = 3^{2}$ $9=3^2$ so:
$3^{2 (x - 1)} = 3^{3}$ $3^(2(x-1))=3^3$
And:
$2 (x - 1) = 3$ $2(x-1)=3$
$2 x - 2 = 3$ $2x-2=3$
$x = \frac{5}{2}$ $x=5/2$

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What is the solution set of $4 [9^{x - 1}] = 108$ $4[9^(x-1)] = 108$ ?

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