Finite Math Examples

Solve for x 8*2^x=81*3^(x-1)
Step 1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2
Expand the left side.
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Step 2.1
Rewrite as .
Step 2.2
Expand by moving outside the logarithm.
Step 3
Expand the right side.
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Step 3.1
Rewrite as .
Step 3.2
Expand by moving outside the logarithm.
Step 4
Simplify the right side.
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Step 4.1
Simplify .
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Step 4.1.1
Simplify each term.
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Step 4.1.1.1
Apply the distributive property.
Step 4.1.1.2
Rewrite as .
Step 4.1.2
Use the quotient property of logarithms, .
Step 4.1.3
Divide by .
Step 5
Reorder and .
Step 6
Move all the terms containing a logarithm to the left side of the equation.
Step 7
Use the quotient property of logarithms, .
Step 8
Subtract from both sides of the equation.
Step 9
Factor out of .
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Step 9.1
Factor out of .
Step 9.2
Factor out of .
Step 9.3
Factor out of .
Step 10
Rewrite as .
Step 11
Divide each term in by and simplify.
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Step 11.1
Divide each term in by .
Step 11.2
Simplify the left side.
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Step 11.2.1
Cancel the common factor of .
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Step 11.2.1.1
Cancel the common factor.
Step 11.2.1.2
Divide by .
Step 11.3
Simplify the right side.
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Step 11.3.1
Move the negative in front of the fraction.
Step 12
The result can be shown in multiple forms.
Exact Form:
Decimal Form: