O lvl A Maths: Indices and Logarithms

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express the following in the form ln x = ax + b and find a and b

(xe^x)² = 30e^-x

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Answer:

(xe^x)² = 30e^-x
2 ln(xe^x) = ln (30e^-x)
2 ln x +2 ln (e^x) = ln 30 + ln (e^-x)
2 ln x + 2x = ln 30 - x

so,
2 ln x = -3x + ln 30
ln x = -1.5x + 0.5 ln 30

thus,
a = -1.5
b = 0.5 ln30 = 1.7

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