Logarithms
Hong Kong
Stage 4 - Stage 5
Solving logarithmic equations
Lesson
In previous chapters we learnt how to evaluate logarithmic expressions in terms of numbers, e.g. $\log_39=2$log39=2. Now let's have a look at how to use logs in algebraic equations to solve things! For example, if we have the expression $\log_3x=2$log3x=2, we would first need to rearrange the expression to make $x$x the subject, just like any other algebraic expression:
| $\log_3x$log3x | $=$= | $2$2 |
| $x$x | $=$= | $3^2$32 |
| $=$= | $9$9 |
Remember!
Use your index laws and log laws to see if you can first simplify your expressions
Examples
question 1
Solve $2^x=5$2x=5 for $x$x.
Give your answer to 2 decimal places if necessary.
question 2
Solve $\log_7y=5$log7y=5 for $y$y.
question 3
Solve $\log_{10}x-\log_{10}38=\log_{10}37$log10x−log1038=log1037 for $x$x.