How do you use the properties of logarithms to find the exact value of ${log}_{2} 6 \cdot {log}_{6} 4$ $log_2 6*log_6 4$ ?

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How do you use the properties of logarithms to find the exact value of ${log}_{2} 6 \cdot {log}_{6} 4$ $log_2 6*log_6 4$ ?

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Answer 1 · 2015-11-16T09:24:02

Using the chain of base rule

${log}_{2} 6 \cdot {log}_{6} 4 = \frac{log 6}{log 2} \cdot \frac{log 4}{log 6} = \frac{log 4}{log 2} = \frac{{log 2}^{2}}{log 2} = 2 \frac{log 2}{log 2} = 2$ $log_2 6*log_6 4=log6/log2*log4/log6=log4/log2=log2^2/log2=2log2/(log2)=2$

The chain of base rule states that

${log}_{a} b = \frac{log b}{log a}$ $log_a b=logb/loga$

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How do you use the properties of logarithms to find the exact value of ${log}_{2} 6 \cdot {log}_{6} 4$ $log_2 6*log_6 4$ ?

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