Use Logarithms To Solve Exponential Equations and Inequalities
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Pre-Calculus › Use Logarithms To Solve Exponential Equations and Inequalities
Simplify the log expression:
Cannot be simplified any further
Explanation
The logarithmic expression is as simplified as can be.
Solving an exponential equation.
Solve for ,
.
Explanation
We recall the property:
Now, .
Thus
.
Solve the equation for using the rules of logarithms.
Explanation
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.
Solve
.
Explanation
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
.
Solve for x in the following equation:
Explanation
Solve the following equation:
Explanation
To solve this equation, recall the following property:
Can be rewritten as
Evaluate with your calculator to get
Solve for x:
Explanation
Solve for x using the rules of logarithms:
Explanation
Solve for x:
Explanation
Solving an exponential equation.
Solve
Explanation
Use (which is just
, by convention) to solve.
.