Logarithmic Functions

Lesson

In previous chapters we learnt how to evaluate logarithmic expressions in terms of numbers, e.g. $\log_39=2$`l``o``g`39=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 $\log_3x=2$`l``o``g`3`x`=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

Solve $2^x=5$2`x`=5 for $x$`x`.

Give your answer to 2 decimal places if necessary.

Solve $\log_7y=5$`l``o``g`7`y`=5 for $y$`y`.

Solve $\log_{10}x-\log_{10}38=\log_{10}37$`l``o``g`10`x`−`l``o``g`1038=`l``o``g`1037 for $x$`x`.

Manipulate rational, exponential, and logarithmic algebraic expressions

Apply algebraic methods in solving problems