Question 89

The value of $$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$ is equal to

Solution

$$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$

$$81 = 3^4$$ and $$0.008 = \frac{8}{1000} = \frac{2^{3}}{10^{3}} = \frac{1}{5^{3}} = 5^{-3} $$

Hence,

$$\log_{0.008}\sqrt{5}+ 8 -7 $$

$$ \log_{5^{-3}}5^{\frac{1}{2}}+ 8 -7 $$

$$\frac{log 5^{0.5}}{log 5^{-3}} + 1$$

$$ - \frac{1}{6} + 1$$

= $$\frac{5}{6}$$

Video Solution

video

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 35+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

cracku

Boost your Prep!

Download App