log(base)3(4x+10)=log(base)3(x+1)

Solution for log(base)3(4x+10)=log(base)3(x+1) equation:

Simplifying
log(base) * 3(4x + 10) = log(base) * 3(x + 1)

Reorder the terms:
glo * abes * 3(10 + 4x) = log(base) * 3(x + 1)

Reorder the terms for easier multiplication:
3glo * abes(10 + 4x) = log(base) * 3(x + 1)

Multiply glo * abes
3abeglos(10 + 4x) = log(base) * 3(x + 1)
(10 * 3abeglos + 4x * 3abeglos) = log(base) * 3(x + 1)
(30abeglos + 12abeglosx) = log(base) * 3(x + 1)

Reorder the terms:
30abeglos + 12abeglosx = glo * abes * 3(1 + x)

Reorder the terms for easier multiplication:
30abeglos + 12abeglosx = 3glo * abes(1 + x)

Multiply glo * abes
30abeglos + 12abeglosx = 3abeglos(1 + x)
30abeglos + 12abeglosx = (1 * 3abeglos + x * 3abeglos)
30abeglos + 12abeglosx = (3abeglos + 3abeglosx)

Solving
30abeglos + 12abeglosx = 3abeglos + 3abeglosx

Solving for variable 'a'.

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

Add '-3abeglos' to each side of the equation.
30abeglos + -3abeglos + 12abeglosx = 3abeglos + -3abeglos + 3abeglosx

Combine like terms: 30abeglos + -3abeglos = 27abeglos
27abeglos + 12abeglosx = 3abeglos + -3abeglos + 3abeglosx

Combine like terms: 3abeglos + -3abeglos = 0
27abeglos + 12abeglosx = 0 + 3abeglosx
27abeglos + 12abeglosx = 3abeglosx

Add '-3abeglosx' to each side of the equation.
27abeglos + 12abeglosx + -3abeglosx = 3abeglosx + -3abeglosx

Combine like terms: 12abeglosx + -3abeglosx = 9abeglosx
27abeglos + 9abeglosx = 3abeglosx + -3abeglosx

Combine like terms: 3abeglosx + -3abeglosx = 0
27abeglos + 9abeglosx = 0

Factor out the Greatest Common Factor (GCF), '9abeglos'.
9abeglos(3 + x) = 0

Ignore the factor 9.
Subproblem 1
Set the factor 'abeglos' equal to zero and attempt to solve:

Simplifying
abeglos = 0

Solving
abeglos = 0

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

Simplifying
abeglos = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Add '-1x' to each side of the equation.
x + -1x = -3 + -1x

Combine like terms: x + -1x = 0
0 = -3 + -1x

Simplifying
0 = -3 + -1x

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.