Trigonometry Examples

Solve for x 3^(x^(2-12))=9^(2x)
Step 1
Create equivalent expressions in the equation that all have equal bases.
Step 2
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Step 3
Solve for .
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Step 3.1
Simplify .
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Step 3.1.1
Rewrite.
Step 3.1.2
Simplify by adding zeros.
Step 3.1.3
Subtract from .
Step 3.1.4
Rewrite the expression using the negative exponent rule .
Step 3.2
Multiply by .
Step 3.3
Subtract from both sides of the equation.
Step 3.4
Find the LCD of the terms in the equation.
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Step 3.4.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.4.2
The LCM of one and any expression is the expression.
Step 3.5
Multiply each term in by to eliminate the fractions.
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Step 3.5.1
Multiply each term in by .
Step 3.5.2
Simplify the left side.
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Step 3.5.2.1
Simplify each term.
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Step 3.5.2.1.1
Cancel the common factor of .
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Step 3.5.2.1.1.1
Cancel the common factor.
Step 3.5.2.1.1.2
Rewrite the expression.
Step 3.5.2.1.2
Multiply by by adding the exponents.
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Step 3.5.2.1.2.1
Move .
Step 3.5.2.1.2.2
Multiply by .
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Step 3.5.2.1.2.2.1
Raise to the power of .
Step 3.5.2.1.2.2.2
Use the power rule to combine exponents.
Step 3.5.2.1.2.3
Add and .
Step 3.5.3
Simplify the right side.
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Step 3.5.3.1
Multiply by .
Step 3.6
Solve the equation.
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Step 3.6.1
Subtract from both sides of the equation.
Step 3.6.2
Divide each term in by and simplify.
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Step 3.6.2.1
Divide each term in by .
Step 3.6.2.2
Simplify the left side.
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Step 3.6.2.2.1
Cancel the common factor of .
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Step 3.6.2.2.1.1
Cancel the common factor.
Step 3.6.2.2.1.2
Divide by .
Step 3.6.2.3
Simplify the right side.
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Step 3.6.2.3.1
Dividing two negative values results in a positive value.
Step 3.6.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.6.4
Simplify .
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Step 3.6.4.1
Rewrite as .
Step 3.6.4.2
Any root of is .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: