ln(x+40)+ln(2)=2ln(x)

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Solution for ln(x+40)+ln(2)=2ln(x) equation:


Simplifying
ln(x + 40) + ln(2) = 2ln(x)

Reorder the terms:
ln(40 + x) + ln(2) = 2ln(x)
(40 * ln + x * ln) + ln(2) = 2ln(x)
(40ln + lnx) + ln(2) = 2ln(x)

Reorder the terms for easier multiplication:
40ln + lnx + 2ln = 2ln(x)

Reorder the terms:
40ln + 2ln + lnx = 2ln(x)

Combine like terms: 40ln + 2ln = 42ln
42ln + lnx = 2ln(x)

Multiply ln * x
42ln + lnx = 2lnx

Solving
42ln + lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
42ln + lnx + -2lnx = 2lnx + -2lnx

Combine like terms: lnx + -2lnx = -1lnx
42ln + -1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
42ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(42 + -1x) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(42 + -1x)' equal to zero and attempt to solve: Simplifying 42 + -1x = 0 Solving 42 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + -1x = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -1x = 0 + -42 -1x = 0 + -42 Combine like terms: 0 + -42 = -42 -1x = -42 Add 'x' to each side of the equation. -1x + x = -42 + x Combine like terms: -1x + x = 0 0 = -42 + x Simplifying 0 = -42 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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