Trigonometry Examples

Solve for x log base 11 of x-7=-5
Step 1
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Simplify .
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Step 2.2.1
Rewrite the expression using the negative exponent rule .
Step 2.2.2
Raise to the power of .
Step 2.3
Move all terms not containing to the right side of the equation.
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Step 2.3.1
Add to both sides of the equation.
Step 2.3.2
To write as a fraction with a common denominator, multiply by .
Step 2.3.3
Combine and .
Step 2.3.4
Combine the numerators over the common denominator.
Step 2.3.5
Simplify the numerator.
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Step 2.3.5.1
Multiply by .
Step 2.3.5.2
Add and .
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: