Find the number of values of x for which 8x+27x12x+18x=76

Sail E0 Webinar

Question

Find the number of values of x for which $\frac{8^{x} + 27^{x}}{12^{x} + 18^{x}} = \frac{7}{6}$

Answer: Option B
:
B
Let

2^{x} = a

and

3^{x} = b,

the equation becomes

\frac{a^{3} + b^{3}}{a^{2 b} + b^{2 a}} = \frac{7}{6}

o r \frac{a^{2} - a b + b^{2}}{a b} = \frac{7}{6}

o r 6 a^{2} - 13 a b + 6 b^{2} = 0

(2 a - 3 b) (3 a - 2 b) = 0

Therefore

2^{x + 1} = 3^{x + 1}

or

2^{x - 1} = 3^{x - 1}

which implies that x= -1 and x= 1. Hence only two solutions exist.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. Two guys Abhinav and Bineesh are walking downward and upward respectively on a descending escalator. Abhinav take....escalator find the difference in steps covered by them when they meet.

Question 2. If N=702730+302780 is divisible by 10x (x is a natural number), find the rightmost non-zero integer in the remainder w....when N is divided by 10x+1 (if x is maximum).

Question 3. When Arpita was going through her address book, she glanced upon the telephone number of her old friend, Gita. However....maximum number of trials till she dials the right number.

Question 4. A 50m long platoon is marching ahead. The last person in the platoon wants to give a letter to the first person leadin....Assuming that he ran the whole distance with uniform speed

Question 5. A number is said to be a 'zeroth number' if the sum of the squares of its digits ends in a zero. How many tw....in a zero. How many two-digit 'zeroth numbers' are there?

Question 6. Let x and y be consecutive integers. Suppose m be the number of solutions of x3−y3=3k2 and n be the number of s....where k, t are integers. Then m + n equals:

Question 7. In the given equilateral triangle, the smaller circle and the bigger semi circle are inscribed inside. What is the value....circle are inscribed inside. What is the value of XY

Question 8. An engine without wagon can go at the rate of 24 kmph and its speed diminishes by a quantity which va....number of wagons with which the wagon can move is :

Question 9. Find the minimum value of a+b+c+d in the equation x5−ax4+bx3−cx2+dx−243=0, if it is giv....it is given that the roots are positive real numbers ?

Question 10. Suppose f(x)=(x+1)2 for x≥1. If g(x) is the function whose graph is reflection of the graph of ....f(x) with respect to the line y = x, then g(x) equals:

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Chapter 3.1 : Overview of Finance & Accounts Department Chapter 3 : Finance & Accounts SAIL E0 - GFM 2024

Chapter 2.1 : Overview Chapter 2 : Materials Management SAIL E0 - GFM 2024

Chapter 1.1 : Personnel Functions- An overview Chapter 1 : Personnel Management SAIL E0 - GFM 2024

GPOE / GPA Combined 1 Free CBT Mock Test SAIL E0 2024

CBT Mixed Test 1 GPOE/GPA SAIL E0 2024