Question

2log 15/2 -log 25/81 +3 log 2/9 =log 2

Answer 1

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Answer 2

$2\log (\dfrac{15}{2})-\log (\dfrac{25}{81})+3\log(\dfrac{2}{9})=\log 2$

Step-by-step explanation:

We need to prove

$2\log (\dfrac{15}{2})-\log (\dfrac{25}{81})+3\log(\dfrac{2}{9})=\log 2$

Taking LHS,

$LHS=2\log (\dfrac{15}{2})-\log (\dfrac{25}{81})+3\log(\dfrac{2}{9})$

Using the properties of logarithm we get

$LHS=\log(\dfrac{15}{2})^2-\log (\dfrac{25}{81})+\log(\dfrac{2}{9})^3$                   $[\because \log a^b=b\log a]$

$LHS=\log(\dfrac{15^2}{2^2}\times \dfrac{2^3}{9^3})-\log (\dfrac{25}{81})$                   $[\because \log ab=\log a+\log b]$

$LHS=\log(\dfrac{50}{81})-\log (\dfrac{25}{81})$

$LHS=\log(\dfrac{\dfrac{50}{81}}{\dfrac{25}{81}})$                     $[\because \log \dfrac{a}{b}=\log a-\log b]$

$LHS=\log(2)$

$LHS=RHS$

Hence proved.

#Learn more

Express in terms of log 2 and log 3 log root 54^1/2 * log 243^1/3

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