Finite Math Examples

Solve for x 6^(3x+2)=7^(x-2)
Step 1
Take the log of both sides of the equation.
Step 2
Expand by moving outside the logarithm.
Step 3
Expand by moving outside the logarithm.
Step 4
Solve the equation for .
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Step 4.1
Simplify .
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Step 4.1.1
Rewrite.
Step 4.1.2
Simplify by adding zeros.
Step 4.1.3
Apply the distributive property.
Step 4.2
Apply the distributive property.
Step 4.3
Subtract from both sides of the equation.
Step 4.4
Subtract from both sides of the equation.
Step 4.5
Factor out of .
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Step 4.5.1
Factor out of .
Step 4.5.2
Factor out of .
Step 4.5.3
Factor out of .
Step 4.6
Rewrite as .
Step 4.7
Divide each term in by and simplify.
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Step 4.7.1
Divide each term in by .
Step 4.7.2
Simplify the left side.
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Step 4.7.2.1
Cancel the common factor of .
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Step 4.7.2.1.1
Cancel the common factor.
Step 4.7.2.1.2
Divide by .
Step 4.7.3
Simplify the right side.
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Step 4.7.3.1
Combine the numerators over the common denominator.
Step 4.7.3.2
Factor out of .
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Step 4.7.3.2.1
Factor out of .
Step 4.7.3.2.2
Factor out of .
Step 4.7.3.2.3
Factor out of .
Step 4.7.3.3
Factor out of .
Step 4.7.3.4
Factor out of .
Step 4.7.3.5
Factor out of .
Step 4.7.3.6
Simplify the expression.
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Step 4.7.3.6.1
Rewrite as .
Step 4.7.3.6.2
Move the negative in front of the fraction.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: