ln(6x+11)+ln(x)=ln(10)

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Solution for ln(6x+11)+ln(x)=ln(10) equation: 


Simplifying
ln(6x + 11) + ln(x) = ln(10)

Reorder the terms:
ln(11 + 6x) + ln(x) = ln(10)
(11 * ln + 6x * ln) + ln(x) = ln(10)
(11ln + 6lnx) + ln(x) = ln(10)

Multiply ln * x
11ln + 6lnx + lnx = ln(10)

Combine like terms: 6lnx + lnx = 7lnx
11ln + 7lnx = ln(10)

Reorder the terms for easier multiplication:
11ln + 7lnx = 10ln

Solving
11ln + 7lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
11ln + -10ln + 7lnx = 10ln + -10ln

Combine like terms: 11ln + -10ln = 1ln
1ln + 7lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
1ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 7x) = 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 '(1 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Add '-7x' to each side of the equation.
7x + -7x = -1 + -7x

Combine like terms: 7x + -7x = 0
0 = -1 + -7x

Simplifying
0 = -1 + -7x

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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