How do you change the base of a logarithm?

Now Playing:Evaluate logarithms using change of base formula– Example 1

How to apply $``$ change-of-base rule $"$

Express $\log_53$ in three different ways.

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Using a calculator, evaluate the following logarithms
by applying $``$ change-of-base rule $":$
1. $\log_53$
  
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2. $\log_7\sqrt{416}$
  
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3. $\log_2\frac{7}{25}$
  
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4. 6 $\log_4999$
  
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Using a calculator, solve for $x$ to the nearest hundredth.
1. $\log_6x = log_7 8$
  
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2. $\log_{23}5 = log_x\sqrt{0.104}$