New Zealand
Level 7 - NCEA Level 2

# 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:

 $\log_3x$log3​x $=$= $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.

##### question 2

Solve $\log_7y=5$log7y=5 for $y$y.

##### question 3

Solve $\log_{10}x-\log_{10}38=\log_{10}37$log10xlog1038=log1037 for $x$x.

### Outcomes

#### M7-6

Manipulate rational, exponential, and logarithmic algebraic expressions

#### 91261

Apply algebraic methods in solving problems