ln(15k+2)=2ln(k)+ln(8)

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Solution for ln(15k+2)=2ln(k)+ln(8) equation:


Simplifying
ln(15k + 2) = 2ln(k) + ln(8)

Reorder the terms:
ln(2 + 15k) = 2ln(k) + ln(8)
(2 * ln + 15k * ln) = 2ln(k) + ln(8)

Reorder the terms:
(15kln + 2ln) = 2ln(k) + ln(8)
(15kln + 2ln) = 2ln(k) + ln(8)

Multiply ln * k
15kln + 2ln = 2kln + ln(8)

Reorder the terms for easier multiplication:
15kln + 2ln = 2kln + 8ln

Solving
15kln + 2ln = 2kln + 8ln

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-2kln' to each side of the equation.
15kln + -2kln + 2ln = 2kln + -2kln + 8ln

Combine like terms: 15kln + -2kln = 13kln
13kln + 2ln = 2kln + -2kln + 8ln

Combine like terms: 2kln + -2kln = 0
13kln + 2ln = 0 + 8ln
13kln + 2ln = 8ln

Add '-2ln' to each side of the equation.
13kln + 2ln + -2ln = 8ln + -2ln

Combine like terms: 2ln + -2ln = 0
13kln + 0 = 8ln + -2ln
13kln = 8ln + -2ln

Combine like terms: 8ln + -2ln = 6ln
13kln = 6ln

Divide each side by '13ln'.
k = 0.4615384615

Simplifying
k = 0.4615384615

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