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Example Questions
Example Question #1 : Use Logarithms To Solve Exponential Equations And Inequalities
Solving an exponential equation.
Solve for ,
.
We recall the property:
Now, .
Thus
.
Example Question #132 : Exponential And Logarithmic Functions
Solving an exponential equation.
Solve
Use (which is just
, by convention) to solve.
.
Example Question #1 : Use Logarithms To Solve Exponential Equations And Inequalities
Solve the equation for using the rules of logarithms.
Expanding the logarithms into sums of logarithms will cancel out the first two x terms, resulting in the equation:
Combining the first and second terms, then subtracting the new term over will allow you to isolate the variable term.
Divide both sides of the equation by 2, then exponentiate with 3.
Evaluating this term numerically will give the correct answer.
Example Question #1 : Use Logarithms To Solve Exponential Equations And Inequalities
Solve the following equation:
To solve this equation, recall the following property:
Can be rewritten as
Evaluate with your calculator to get
Example Question #141 : Exponential And Logarithmic Functions
Solve
.
After using the division rule to simplify the left hand side you can take the natural log of both sides.
If you then combine like terms you get a quadratic equation which factors to,
.
Setting each binomial equal to zero and solving for we get the solution to be
.
Example Question #1 : Exponential Equations And Inequalities
Solve for x:
Example Question #1 : Exponential Equations And Inequalities
Solve for x in the following equation:
Example Question #141 : Exponential And Logarithmic Functions
Solve for x using the rules of logarithms:
Example Question #142 : Exponential And Logarithmic Functions
Solve for x:
Example Question #3 : Exponential Equations And Inequalities
Simplify the log expression:
Cannot be simplified any further
Cannot be simplified any further
The logarithmic expression is as simplified as can be.
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