Question 92

If m and n are integers such that $$(\surd2)^{19} 3^4 4^2 9^m 8^n = 3^n 16^m (\sqrt[4]{64})$$ then m is

Solution

We have, $$(\surd2)^{19} 3^4 4^2 9^m 8^n = 3^n 16^m (\sqrt[4]{64})$$

Converting both sides in powers of 2 and 3, we get

$$2^{\ \frac{19\ }{2}}3^42^43^{2m}2^{3n}$$ = $$3^n2^{4m}2^{\frac{\ 6}{4}}$$

Comparing the power of 2 we get, $$\ \frac{\ 19}{2}+4+3n\ =4m+\frac{\ 6}{4}\ $$

=> 4m=3n+12 .....(1)

Comparing the power of 3 we get, $$4+2m=n$$

Substituting the value of n in (1), we get

4m=3(4+2m)+12

=> m=-12

Video Solution

video

Click on the Email ☝️ to Watch the Video Solution

Create a FREE account and get:

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

CAT Quant Questions | CAT Quantitative Ability

CAT Progressions and Series Questions CAT Profit, Loss and Interest Questions CAT Algebra Questions CAT Averages Mixtures Alligations Questions CAT Percentages Questions

CAT DILR Questions | LRDI Questions For CAT

CAT DI with connected data sets Questions CAT Games and Tournamnents Questions CAT Venn Diagrams Questions CAT Quant Based LR Questions CAT Special Charts Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Odd One Out Questions CAT Vocabulary Questions CAT Para Summary Questions CAT Reading Comprehension Questions CAT Grammar and Sentence Correction Questions

Follow us on

Boost your Prep!

Download App