Trigonometry Examples

Solve for t 10000=22500*10^(-t/12)
Step 1
Rewrite the equation as .
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Cancel the common factor of and .
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Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factors.
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Step 2.3.1.2.1
Factor out of .
Step 2.3.1.2.2
Cancel the common factor.
Step 2.3.1.2.3
Rewrite the expression.
Step 3
Take the base logarithm of both sides of the equation to remove the variable from the exponent.
Step 4
Expand the left side.
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Step 4.1
Expand by moving outside the logarithm.
Step 4.2
Logarithm base of is .
Step 4.3
Multiply by .
Step 5
Multiply both sides of the equation by .
Step 6
Simplify the left side.
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Step 6.1
Simplify .
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Step 6.1.1
Cancel the common factor of .
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Step 6.1.1.1
Move the leading negative in into the numerator.
Step 6.1.1.2
Factor out of .
Step 6.1.1.3
Cancel the common factor.
Step 6.1.1.4
Rewrite the expression.
Step 6.1.2
Multiply.
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Step 6.1.2.1
Multiply by .
Step 6.1.2.2
Multiply by .
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: