Finite Math Examples

Solve for b log base b of 3=0.517
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
Convert the decimal exponent to a fractional exponent.
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Step 2.1.1
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are numbers to the right of the decimal point, place the decimal number over . Next, add the whole number to the left of the decimal.
Step 2.1.2
Convert to an improper fraction.
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Step 2.1.2.1
A mixed number is an addition of its whole and fractional parts.
Step 2.1.2.2
Add and .
Step 2.2
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Step 2.3
Simplify the exponent.
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Step 2.3.1
Simplify the left side.
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Step 2.3.1.1
Simplify .
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Step 2.3.1.1.1
Multiply the exponents in .
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Step 2.3.1.1.1.1
Apply the power rule and multiply exponents, .
Step 2.3.1.1.1.2
Cancel the common factor of .
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Step 2.3.1.1.1.2.1
Factor out of .
Step 2.3.1.1.1.2.2
Cancel the common factor.
Step 2.3.1.1.1.2.3
Rewrite the expression.
Step 2.3.1.1.1.3
Divide by .
Step 2.3.1.1.2
Simplify.
Step 2.3.2
Simplify the right side.
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Step 2.3.2.1
Simplify .
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Step 2.3.2.1.1
Divide by .
Step 2.3.2.1.2
Raise to the power of .