Algebra Examples

Solve for x ((y^(2x))/(y^6))^-1=(y^-3)^4
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
Expand by moving outside the logarithm.
Step 2.2
Reduce the expression by cancelling the common factors.
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Step 2.2.1
Factor out of .
Step 2.2.2
Multiply by .
Step 2.2.3
Cancel the common factor.
Step 2.2.4
Rewrite the expression.
Step 2.3
Divide by .
Step 2.4
Expand by moving outside the logarithm.
Step 3
Simplify the left side.
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Step 3.1
Simplify .
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Step 3.1.1
Apply the distributive property.
Step 3.1.2
Apply the distributive property.
Step 3.1.3
Multiply.
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Step 3.1.3.1
Multiply by .
Step 3.1.3.2
Multiply by .
Step 4
Simplify the right side.
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Step 4.1
Simplify .
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Step 4.1.1
Multiply the exponents in .
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Step 4.1.1.1
Apply the power rule and multiply exponents, .
Step 4.1.1.2
Multiply by .
Step 4.1.2
Rewrite the expression using the negative exponent rule .
Step 5
Move all the terms containing a logarithm to the left side of the equation.
Step 6
Move all terms not containing to the right side of the equation.
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Step 6.1
Subtract from both sides of the equation.
Step 6.2
Add to both sides of the equation.
Step 7
Divide each term in by and simplify.
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Step 7.1
Divide each term in by .
Step 7.2
Simplify the left side.
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Step 7.2.1
Cancel the common factor of .
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Step 7.2.1.1
Cancel the common factor.
Step 7.2.1.2
Rewrite the expression.
Step 7.2.2
Cancel the common factor of .
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Step 7.2.2.1
Cancel the common factor.
Step 7.2.2.2
Divide by .
Step 7.3
Simplify the right side.
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Step 7.3.1
Simplify each term.
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Step 7.3.1.1
Cancel the common factor of and .
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Step 7.3.1.1.1
Factor out of .
Step 7.3.1.1.2
Cancel the common factors.
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Step 7.3.1.1.2.1
Factor out of .
Step 7.3.1.1.2.2
Cancel the common factor.
Step 7.3.1.1.2.3
Rewrite the expression.
Step 7.3.1.2
Cancel the common factor of .
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Step 7.3.1.2.1
Cancel the common factor.
Step 7.3.1.2.2
Divide by .
Step 7.3.1.3
Move the negative in front of the fraction.