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Popular >

simplify ln(4/(e^{3x-1)})

Solution

simplify

ln (\frac{4}{e ^{3 x - 1}})

Solution

2 ln (2) - 3 x + 1

Solution steps

ln (\frac{4}{e ^{3 x - 1}})

Apply log rule:

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

ln (\frac{4}{e ^{3 x - 1}}) = ln (4) - ln (e^{3 x - 1})

= ln (4) - ln (e^{3 x - 1})

Apply log rule:

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

ln (e^{3 x - 1}) = (3 x - 1) ln (e)

= ln (4) - (3 x - 1) ln (e)

(3 x - 1) ln (e) = 3 x - 1

= ln (4) - (3 x - 1)

ln (4) = 2 ln (2)

= 2 ln (2) - (3 x - 1)

- (3 x - 1) : - 3 x + 1

= 2 ln (2) - 3 x + 1

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Frequently Asked Questions (FAQ)

What is ln(4/(e^{3x-1)}) ?
The solution to ln(4/(e^{3x-1)}) is 2ln(2)-3x+1