Basic Math Examples

Solve for q 3*12^q=2^(q-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 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
Apply the distributive property.
Step 4.1.2
Rewrite as .
Step 5
Reorder and .
Step 6
Move all the terms containing a logarithm to the left side of the equation.
Step 7
Use the product property of logarithms, .
Step 8
Multiply by .
Step 9
Subtract from both sides of the equation.
Step 10
Factor out of .
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Step 10.1
Factor out of .
Step 10.2
Factor out of .
Step 10.3
Factor out of .
Step 11
Rewrite as .
Step 12
Divide each term in by and simplify.
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Step 12.1
Divide each term in by .
Step 12.2
Simplify the left side.
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Step 12.2.1
Cancel the common factor of .
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Step 12.2.1.1
Cancel the common factor.
Step 12.2.1.2
Divide by .
Step 12.3
Simplify the right side.
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Step 12.3.1
Move the negative in front of the fraction.
Step 13
The result can be shown in multiple forms.
Exact Form:
Decimal Form: