Finite Math Examples

Solve by Factoring 3(9)^(x-3)=25
Step 1
Subtract from both sides of the equation.
Step 2
Multiply .
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Step 2.1
Rewrite as .
Step 2.2
Multiply the exponents in .
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Step 2.2.1
Apply the power rule and multiply exponents, .
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Multiply by .
Step 2.3
Use the power rule to combine exponents.
Step 2.4
Subtract from .
Step 3
Add to both sides of the equation.
Step 4
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 5
Expand by moving outside the logarithm.
Step 6
Simplify the left side.
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Step 6.1
Apply the distributive property.
Step 7
Move all the terms containing a logarithm to the left side of the equation.
Step 8
Move all terms not containing to the right side of the equation.
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Step 8.1
Add to both sides of the equation.
Step 8.2
Add to both sides of the equation.
Step 9
Divide each term in by and simplify.
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Step 9.1
Divide each term in by .
Step 9.2
Simplify the left side.
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Step 9.2.1
Cancel the common factor of .
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Step 9.2.1.1
Cancel the common factor.
Step 9.2.1.2
Rewrite the expression.
Step 9.2.2
Cancel the common factor of .
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Step 9.2.2.1
Cancel the common factor.
Step 9.2.2.2
Divide by .
Step 9.3
Simplify the right side.
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Step 9.3.1
Cancel the common factor of .
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Step 9.3.1.1
Cancel the common factor.
Step 9.3.1.2
Rewrite the expression.
Step 10
Simplify each term.
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Step 10.1
Rewrite as .
Step 10.2
Expand by moving outside the logarithm.
Step 10.3
Cancel the common factor of .
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Step 10.3.1
Cancel the common factor.
Step 10.3.2
Rewrite the expression.