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
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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 |