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New Zealand
Level 7 - NCEA Level 2

Solving logarithmic equations


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

Use your index laws and log laws to see if you can first simplify your expressions



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



Manipulate rational, exponential, and logarithmic algebraic expressions


Apply algebraic methods in solving problems

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