Finite Math Examples

Solve for x 5(1.06^(2x+1))=11
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 3
Expand by moving outside the logarithm.
Step 4
Simplify the left side.
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Step 4.1
Simplify .
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Step 4.1.1
Apply the distributive property.
Step 4.1.2
Multiply by .
Step 5
Move all the terms containing a logarithm to the left side of the equation.
Step 6
Use the quotient property of logarithms, .
Step 7
Simplify each term.
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Step 7.1
Multiply the numerator by the reciprocal of the denominator.
Step 7.2
Multiply .
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Step 7.2.1
Combine and .
Step 7.2.2
Multiply by .
Step 7.3
Divide by .
Step 8
Subtract from 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
Move the negative in front of the fraction.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: