What is ln((2^{0.538-1}-1)/((0.538-1)x)) ?

The solution to ln((2^{0.538-1}-1)/((0.538-1)x)) is ln(1/(2^{0.462)}-1)-ln(-0.462)-ln(x)

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simplify ln((2^{0.538-1}-1)/((0.538-1)x))

simplify

ln (\frac{2 ^{0.538 - 1} - 1}{( 0.538 - 1 ) x})

ln (\frac{1}{2 ^{0.462}} - 1) - ln (- 0.462) - ln (x)

Solution steps

ln (\frac{2 ^{0.538 - 1} - 1}{( 0.538 - 1 ) x})

Apply log rule:

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

ln (\frac{2 ^{0.538 - 1} - 1}{( 0.538 - 1 ) x}) = ln (2^{0.538 - 1} - 1) - ln ((0.538 - 1) x)

= ln (2^{0.538 - 1} - 1) - ln ((0.538 - 1) x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln ((0.538 - 1) x) = ln (0.538 - 1) + ln (x)

= ln (2^{0.538 - 1} - 1) - (ln (x) + ln (0.538 - 1))

2^{0.538 - 1} = \frac{1}{2 ^{0.462}}

= ln (\frac{1}{2 ^{0.462}} - 1) - (ln (x) + ln (0.538 - 1))

Subtract the numbers:

0.538 - 1 = - 0.462

= ln (\frac{1}{2 ^{0.462}} - 1) - (ln (x) + ln (- 0.462))

- (ln (- 0.462) + ln (x)) : - ln (- 0.462) - ln (x)

= ln (\frac{1}{2 ^{0.462}} - 1) - ln (- 0.462) - ln (x)

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What is ln((2^{0.538-1}-1)/((0.538-1)x)) ?
The solution to ln((2^{0.538-1}-1)/((0.538-1)x)) is ln(1/(2^{0.462)}-1)-ln(-0.462)-ln(x)