Trigonometry Examples

Solve for x ( square root of 6)^(8x)=216^(x-3)
Step 1
Use to rewrite as .
Step 2
Apply the power rule and multiply exponents, .
Step 3
Create equivalent expressions in the equation that all have equal bases.
Step 4
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Step 5
Solve for .
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Step 5.1
Simplify .
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Step 5.1.1
Rewrite.
Step 5.1.2
Simplify by adding zeros.
Step 5.1.3
Cancel the common factor of .
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Step 5.1.3.1
Factor out of .
Step 5.1.3.2
Cancel the common factor.
Step 5.1.3.3
Rewrite the expression.
Step 5.2
Simplify .
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Step 5.2.1
Apply the distributive property.
Step 5.2.2
Multiply by .
Step 5.3
Move all terms containing to the left side of the equation.
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Step 5.3.1
Subtract from both sides of the equation.
Step 5.3.2
Subtract from .