Trigonometry Examples

Solve for x (1/16)^(3x-4)=64^(x-1)
Step 1
Apply the product rule to .
Step 2
One to any power is one.
Step 3
Move to the numerator using the negative exponent rule .
Step 4
Create equivalent expressions in the equation that all have equal bases.
Step 5
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Step 6
Solve for .
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Step 6.1
Simplify .
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Step 6.1.1
Rewrite.
Step 6.1.2
Simplify by adding zeros.
Step 6.1.3
Apply the distributive property.
Step 6.1.4
Multiply.
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Step 6.1.4.1
Multiply by .
Step 6.1.4.2
Multiply by .
Step 6.1.5
Apply the distributive property.
Step 6.1.6
Multiply.
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Step 6.1.6.1
Multiply by .
Step 6.1.6.2
Multiply by .
Step 6.2
Simplify .
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Step 6.2.1
Apply the distributive property.
Step 6.2.2
Multiply by .
Step 6.3
Move all terms containing to the left side of the equation.
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Step 6.3.1
Subtract from both sides of the equation.
Step 6.3.2
Subtract from .
Step 6.4
Move all terms not containing to the right side of the equation.
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Step 6.4.1
Subtract from both sides of the equation.
Step 6.4.2
Subtract from .
Step 6.5
Divide each term in by and simplify.
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Step 6.5.1
Divide each term in by .
Step 6.5.2
Simplify the left side.
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Step 6.5.2.1
Cancel the common factor of .
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Step 6.5.2.1.1
Cancel the common factor.
Step 6.5.2.1.2
Divide by .
Step 6.5.3
Simplify the right side.
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Step 6.5.3.1
Dividing two negative values results in a positive value.
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: