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Popular >

simplify ln((x+1)/(e^{5x)})

Solution

simplify

ln (\frac{x + 1}{e ^{5 x}})

Solution

ln (x + 1) - 5 x

Solution steps

ln (\frac{x + 1}{e ^{5 x}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x + 1}{e ^{5 x}}) = ln (x + 1) - ln (e^{5 x})

= ln (x + 1) - ln (e^{5 x})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{5 x}) = 5 x ln (e)

= ln (x + 1) - 5 x ln (e)

5 x ln (e) = 5 x

= ln (x + 1) - 5 x

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Frequently Asked Questions (FAQ)

What is ln((x+1)/(e^{5x)}) ?
The solution to ln((x+1)/(e^{5x)}) is ln(x+1)-5x