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# Logarithms

## Applications

A logarithmic function can be used to transform an exponential function into a linear one. For example, by applying ln to both sides of we get

.

### Example 3.

Find x such that

Click on the question mark to see the next step in the solution process:

Hint: Apply ln to both sides

### Exercise 3.

 Equation Answer exp( + x) = x = (2 d.p.)

### Example 4.

Solve the equation

Click on the question mark to see the next step in the solution process:

Hint: Apply exp to both sides

### Exercise 4.

 Equation Answer ln( x + ) = x =

### Example 5.

Solve the equation

Click on the question mark to see the next step in the solution process:

Hint: Apply ln to both sides

### Exercise 5.

 Equation Answer x      = x = (2 d.p.)

All logarithmic functions can be transformed to a function involving the natural log.

### Example 6.

Suppose    .

Then

By taking ln of both sides we can solve for y.

Click on the question marks to see the step-by-step solution:

### Exercise 6.

Express the function in terms of the natural log, using fractional answers, not decimals:

e.g. The function  y =(1/2)log2x  expressed in terms of the natural log is y =(1/2)lnx/ln2

Don't type any blank spaces in your answer, and put brackets around any fractional numbers.

 Function Answer y = log x y =