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Embed code for: 4.5 7th Ed Complete
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Summary of Rules and Laws:
logbAC = C logbA
log AC = C log A
lnAC = C lnA
logAAC = C logAA = C
log x = y 10y = x
ln x = y ey = x
logax = y ay = x
ln ey = y
Exponential and Logarithmic Equations
An exponential equation is one in which the variable occurs in the exponent.
Some exponential equations can be solved by using the fact that exponential functions are one-to-one. This means that
ax = ay x = y
Guidelines for Solving Exponential Equations
Isolate the exponential expression on one side of the equation.
Take the logarithm of each side, and then use the Laws of Logarithms to “bring down the exponent.”
Solve for the variable.
Solve the equation:
10x = 121.
(a) Find the exact solution of the equation expressed in terms of logarithms.
(b) Use a calculator to find an approximation to the solution rounded to six decimal places.
Consider the exponential equation
Find the exact solution and the approximate solution.
A logarithmic equation is one in which a logarithm of the variable occurs.
Some logarithmic equations can be solved by using the fact that logarithmic functions are one-to-one.
This means that
logax = logay x = y
Guidelines for Solving Logarithmic Equations
Isolate the logarithmic term on one side of the equation.
You may first need to combine the logarithmic terms.
Write the equation in exponential form (or raise the base to each side).
Solve the equation for x.
Solve the equation:
Using logs to find an inverse
Find the inverse of f.
Types of Interest
If a principal P is invested at an interest rate r for a period of t years, the amount A of the investment is given by: