Trigonometry Examples

Solve for x 5 log of x+1+10=10 log of t+1+5
Step 1
Move all the terms containing a logarithm to the left side of the equation.
Step 2
Add and .
Step 3
Simplify the left side.
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Step 3.1
Simplify .
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Step 3.1.1
Simplify each term.
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Step 3.1.1.1
Simplify by moving inside the logarithm.
Step 3.1.1.2
Simplify by moving inside the logarithm.
Step 3.1.2
Use the quotient property of logarithms, .
Step 4
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 5
Solve for .
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Step 5.1
Rewrite the equation as .
Step 5.2
Multiply both sides by .
Step 5.3
Simplify.
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Step 5.3.1
Simplify the left side.
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Step 5.3.1.1
Cancel the common factor of .
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Step 5.3.1.1.1
Cancel the common factor.
Step 5.3.1.1.2
Rewrite the expression.
Step 5.3.2
Simplify the right side.
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Step 5.3.2.1
Simplify .
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Step 5.3.2.1.1
Rewrite the expression using the negative exponent rule .
Step 5.3.2.1.2
Raise to the power of .
Step 5.3.2.1.3
Combine and .
Step 5.4
Solve for .
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Step 5.4.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5.4.2
Simplify .
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Step 5.4.2.1
Rewrite as .
Step 5.4.2.2
Rewrite as .
Step 5.4.2.3
Rewrite as .
Step 5.4.2.4
Pull terms out from under the radical, assuming real numbers.
Step 5.4.3
Subtract from both sides of the equation.
Step 5.4.4
Simplify .
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Step 5.4.4.1
To write as a fraction with a common denominator, multiply by .
Step 5.4.4.2
Simplify terms.
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Step 5.4.4.2.1
Combine and .
Step 5.4.4.2.2
Combine the numerators over the common denominator.
Step 5.4.4.3
Simplify the numerator.
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Step 5.4.4.3.1
Rewrite as .
Step 5.4.4.3.2
Expand using the FOIL Method.
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Step 5.4.4.3.2.1
Apply the distributive property.
Step 5.4.4.3.2.2
Apply the distributive property.
Step 5.4.4.3.2.3
Apply the distributive property.
Step 5.4.4.3.3
Simplify and combine like terms.
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Step 5.4.4.3.3.1
Simplify each term.
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Step 5.4.4.3.3.1.1
Multiply by .
Step 5.4.4.3.3.1.2
Multiply by .
Step 5.4.4.3.3.1.3
Multiply by .
Step 5.4.4.3.3.1.4
Multiply by .
Step 5.4.4.3.3.2
Add and .
Step 5.4.4.3.4
Multiply by .
Step 5.4.4.3.5
Subtract from .