Calculate logarithms without a calculator

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Now Playing:Evaluate logarithms without a calculator – Example 1a

Evaluate:
1. $\log_832$
2. $\log_51$
  [useful rule: $\log_b1 = 0]$
3. $\log_55$
  [useful rule: $\log_bb = 1]$
4. -3 $\log_{16}1024$
5. $\log_3 (\frac{1}{81})$
6. $\log_2 {^5}\sqrt{64}$
A Logarithmic Expression As An Exponent
Evaluate:
1. ${3^{log_39}}$
  [useful rule: ${b^{log_ba}} = a]$
2. ${2^{log_21024}}$
evaluate:
$\log_{25} \sqrt{125}$
without using a calculator, determine which logarithmic expression has a bigger value:

$\log_220$
vs.
$\log_380$