Evaluating logarithms without a calculator

Evaluating logarithms without a calculator

Lessons

• 1.
Evaluate:
a)
$\log_832$

b)
$\log_51$
[useful rule: $\log_b1 = 0]$

c)
$\log_55$
[useful rule: $\log_bb = 1]$

d)
-3$\log_{16}1024$

e)
$\log_3 (\frac{1}{81})$

f)
$\log_2 {^5}\sqrt{64}$

• 2.
A Logarithmic Expression As An Exponent
Evaluate:
a)
${3^{log_39}}$
[useful rule: ${b^{log_ba}} = a]$

b)
${2^{log_21024}}$

• 3.
evaluate:
$\log_{25} \sqrt{125}$

• 4.
without using a calculator, determine which logarithmic expression has a bigger value:
$\log_220$
vs.
$\log_380$
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