First slide

Introduction to sets

Question

$Given \log_{10} 2 = a and \log_{10} 3 = b . If 3^{x + 2} = 45, then the value of \frac{1 - a}{b} =$

Moderate

A

$\frac{x}{2}$
B

$x$
C

$2 x$
D

$\frac{x}{6}$

Solution

$\begin{array}{l} Given that \log_{10} 2 = a and \log_{10} 3 = b \\ g i v e n t h a t 3^{x + 2} = 45 \Rightarrow (x + 2) \log {}_{3}3 = \log {}_{3}45 \Rightarrow x + 2 = \log_{3} 9 + \log_{3} 5 = 2 + \log_{3} 5 \\ \Rightarrow x = \log_{3} 5 \\ Consider \frac{1 - a}{b} = \frac{1 - \log_{10} 2}{\log_{10} 3} \\ = \frac{\log_{10} 10 - \log_{10} 2}{\log_{10} 3} \\ = \frac{\log_{10} 5}{\log_{10} 3} \\ = \log_{3} 5 \\ = x \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App