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3²x+³(3x-²)=81 solve exponential equation

User XWaZzo
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1 Answer

7 votes

Since you mention "exponential", I suspect the equation is supposed to read


3^(2x+3) 3^(x-2) = 81

Recall that
a^ba^c = a^(b+c), so we can simplify the left side to get


3^((2x+3)+(x-2)) = 81

and since 81 = 3⁴,


3^((2x+3)+(x-2)) = 3^4 \implies (2x+3) + (x - 2) = 4

because the bases in the expressions on either side are the same.

Solve for x :

(2x + 3) + (x - 2) = 4

3x + 1 = 4

3x = 3

x = 1

User Jenica
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