The value of the expression log -7-log 1 - -3 is

Given: log_ππ^7+log_1/ππ^3 Now, assuming nbsp; a = log_ππ^7 ⇒π^a = π^7 ⇒ a =7 b = nbsp;log_1/ππ^3 ⇒(1π)^b = π^3 ⇒π^ b = π^3⇒ b = 3 Therefore log_ππ^7+log ...

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Standard XI

Mathematics

Standard Logarithm

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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Standard Logarithm

Standard XI Mathematics

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The value of the expression logππ7+log1/ππ3 is

Given: logππ7+log1/ππ3 Now, assuming a=logππ7⇒πa=π7⇒a=7b=log1/ππ3⇒(1π)b=π3⇒π−b=π3⇒b=−3 Therefore logππ7+log1/ππ3=a+b=7−3=4

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