ln(17)=ln(2)+ln(x+5)

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Solution for ln(17)=ln(2)+ln(x+5) equation:


Simplifying
ln(17) = ln(2) + ln(x + 5)

Reorder the terms for easier multiplication:
17ln = ln(2) + ln(x + 5)

Reorder the terms for easier multiplication:
17ln = 2ln + ln(x + 5)

Reorder the terms:
17ln = 2ln + ln(5 + x)
17ln = 2ln + (5 * ln + x * ln)
17ln = 2ln + (5ln + lnx)

Combine like terms: 2ln + 5ln = 7ln
17ln = 7ln + lnx

Solving
17ln = 7ln + lnx

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
17ln + -7ln = 7ln + -7ln + lnx

Combine like terms: 17ln + -7ln = 10ln
10ln = 7ln + -7ln + lnx

Combine like terms: 7ln + -7ln = 0
10ln = 0 + lnx
10ln = lnx

Add '-1lnx' to each side of the equation.
10ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
10ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(10 + -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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + 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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