xln(3)*ln(6)=ln(7)*(-5x)

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Solution for xln(3)*ln(6)=ln(7)*(-5x) equation: 


Simplifying
xln(3) * ln(6) = ln(7)(-5x)

Reorder the terms for easier multiplication:
3 * 6lnx * ln = ln(7)(-5x)

Multiply 3 * 6
18lnx * ln = ln(7)(-5x)

Multiply lnx * ln
18l2n2x = ln(7)(-5x)

Remove parenthesis around (-5x)
18l2n2x = ln * 7 * -5x

Reorder the terms for easier multiplication:
18l2n2x = 7 * -5ln * x

Multiply 7 * -5
18l2n2x = -35ln * x

Multiply ln * x
18l2n2x = -35lnx

Solving
18l2n2x = -35lnx

Solving for variable 'l'.

Reorder the terms:
35lnx + 18l2n2x = -35lnx + 35lnx

Combine like terms: -35lnx + 35lnx = 0
35lnx + 18l2n2x = 0

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(35 + 18ln) = 0


Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve:

Simplifying
lnx = 0

Solving
lnx = 0

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

Simplifying
lnx = 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 '(35 + 18ln)' equal to zero and attempt to solve:

Simplifying
35 + 18ln = 0

Solving
35 + 18ln = 0

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

Add '-35' to each side of the equation.
35 + -35 + 18ln = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 18ln = 0 + -35
18ln = 0 + -35

Combine like terms: 0 + -35 = -35
18ln = -35

Divide each side by '18n'.
l = -1.944444444n-1

Simplifying
l = -1.944444444n-1
Solution
l = {-1.944444444n-1}

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