Trigonometry Examples

Solve for x 6 log base 4 of 4x+5+2=5
Step 1
Move all terms not containing to the right side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from .
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Cancel the common factor of and .
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Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factors.
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Step 2.3.1.2.1
Factor out of .
Step 2.3.1.2.2
Cancel the common factor.
Step 2.3.1.2.3
Rewrite the expression.
Step 3
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 4
Solve for .
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Step 4.1
Rewrite the equation as .
Step 4.2
Simplify .
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Step 4.2.1
Rewrite.
Step 4.2.2
Simplify the expression.
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Step 4.2.2.1
Rewrite as .
Step 4.2.2.2
Apply the power rule and multiply exponents, .
Step 4.2.3
Cancel the common factor of .
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Step 4.2.3.1
Cancel the common factor.
Step 4.2.3.2
Rewrite the expression.
Step 4.2.4
Evaluate the exponent.
Step 4.3
Move all terms not containing to the right side of the equation.
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Step 4.3.1
Subtract from both sides of the equation.
Step 4.3.2
Subtract from .
Step 4.4
Divide each term in by and simplify.
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Step 4.4.1
Divide each term in by .
Step 4.4.2
Simplify the left side.
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Step 4.4.2.1
Cancel the common factor of .
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Step 4.4.2.1.1
Cancel the common factor.
Step 4.4.2.1.2
Divide by .
Step 4.4.3
Simplify the right side.
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Step 4.4.3.1
Move the negative in front of the fraction.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: