Finite Math Examples

Solve for x ( square root of 2)^(x+7)=8^x
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
Apply the distributive property.
Step 5.1.4
Combine and .
Step 5.1.5
Combine and .
Step 5.2
Move all terms containing to the left side of the equation.
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Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
To write as a fraction with a common denominator, multiply by .
Step 5.2.3
Combine and .
Step 5.2.4
Combine the numerators over the common denominator.
Step 5.2.5
Combine the numerators over the common denominator.
Step 5.2.6
Multiply by .
Step 5.2.7
Subtract from .
Step 5.2.8
Factor out of .
Step 5.2.9
Rewrite as .
Step 5.2.10
Factor out of .
Step 5.2.11
Rewrite as .
Step 5.2.12
Move the negative in front of the fraction.
Step 5.3
Set the numerator equal to zero.
Step 5.4
Solve the equation for .
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Step 5.4.1
Add to both sides of the equation.
Step 5.4.2
Divide each term in by and simplify.
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Step 5.4.2.1
Divide each term in by .
Step 5.4.2.2
Simplify the left side.
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Step 5.4.2.2.1
Cancel the common factor of .
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Step 5.4.2.2.1.1
Cancel the common factor.
Step 5.4.2.2.1.2
Divide by .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: