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Fundamental Laws of Logarithms

The value of ...

Question

The value of the expression ${log}_{π} π^{7} + {log}_{1 / π} π^{3}$ is

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Solution

Given:
${log}_{π} π^{7} + {log}_{1 / π} π^{3}$
Now, assuming
$a = {log}_{π} π^{7} \Rightarrow π^{a} = π^{7} \Rightarrow a = 7 b = {log}_{1 / π} π^{3} \Rightarrow {(\frac{1}{π})}^{b} = π^{3} \Rightarrow π^{- b} = π^{3} \Rightarrow b = - 3$
Therefore
${log}_{π} π^{7} + {log}_{1 / π} π^{3} = a + b = 7 - 3 = 4$

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Fundamental Laws of Logarithms

Standard XII Mathematics

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