Dr. J's Maths.com
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Functions - Logarithmic function - Concept and simplifying expressions.
Test Yourself 1 - Solutions.


1. Change each of the following expressions from exponential to logarithmic form:

9 = 32

log3 9 = 2

10,000 = 104

log10 10,000 = 4

x = a2

loga x = 2

a = b(2x-1)

logb a = (2x-1)

(3z+1) = 10x

log10 (3z+1) = x

(x - y) = m5

logm (x-y) = 5

2. Express the value for x when 5x = 4 as an expression in log5.

x = log5 4.

 

3. Change each of the following expressions from logarithmic to exponential form and simplify for x:

log2 x = 8

x = 28 = 256

log5 x = 0

x = 50 = 1

log3 x = -2

x = 3-2 = 1/9

log10 (2x) = 2

2x = 102

2x = 100

x = 50

log4 (x-1) = 1

x-1 = 41 = 4

x = 5

 

4. Evaluate each of the following without using a calculator

log2 128

let log2 128 = x

128 = 2x

27 = 2x

so x = 7

log9 3

let log9 3 = x

3 = 9x

31 = 32x

so x = ½

logm m

let logm m = x

m1 = mx

x = 1

log4 0.25

log4 0.25 = x

0.25 = 4x

0.25 = ¼ = 4-1 = 4x

so x = -1

3 log525

let x = log5 25

5x = 25 = 52

x = 2

so 3 log525 = 3 × 2 = 6

5.

Show that elnx = x.

Let a = elnx

loge a = loge x

a = elnx = x

 

Write down the value of eln 5

Using the same strategy as in the previous question:

eln 5 = 5

Evaluate 4eln3

Using the same strategy as in the previous questions:

eln3 = 3

so 4eln3 = 12