True or false I

Algebra Level 3

True or false :

For all positive numbers $a$ and $b$ ,

$\Large{\color{#EC7300}{a} ^{\ln \color{magenta} {b}}=\color{magenta}{b}^{\ln\color{#EC7300}{ a}}}$

False True

1 solution

Rohit Udaiwal
Dec 8, 2015

The easiest way to see this is to log both sides,i.e. $\color{#EC7300}{a} ^{\ln \color{magenta} {b}}=\color{magenta}{b}^{\ln\color{#EC7300}{ a}} \\ \ln(\color{#EC7300}{a}^{\ln\color{magenta}{b}})=\ln( \color{magenta}{b}^{\ln \color{#EC7300}{a}}) \\ (\ln \color{#EC7300}{a})(\ln \color{magenta}{b})=(\ln \color{#EC7300}{a})(\ln \color{magenta}{b}).$

yes! same way. upvoted.

Aareyan Manzoor - 5 years, 6 months ago

True or false I

1 solution

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