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Finite Math Examples
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
Step 2.1
Convert the decimal exponent to a fractional exponent.
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.
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.
Step 2.3.1
Simplify the left side.
Step 2.3.1.1
Simplify .
Step 2.3.1.1.1
Multiply the exponents in .
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 .
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.
Step 2.3.2.1
Simplify .
Step 2.3.2.1.1
Divide by .
Step 2.3.2.1.2
Raise to the power of .