Question

5^(X+2)=7^(X-3)

Answer 1

okay so take Natural log of both sides:
Ln[5^(X+2)] = Ln[7^(X-3)]

Answer 2

Now remember this rule:
LnA^b = b*LnA, so apply it here:
(x+2)*Ln5 = (x-3)*Ln7

Answer 3

Multiply them out:
xLn5 + 2Ln5 = xLn7 - 3Ln7

Answer 4

move terms with x to one side and the ones without to the other side:
xLn5-xLn7 = -3Ln7-2Ln5
Take x out from the left:
x(Ln5-Ln7) = -3Ln7 - 2Ln5

Answer 5

x = (-3Ln7 - 2Ln5)/(Ln5-Ln7)

Answer 6

thanks so much

Answer 7

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Answer 8

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