Question

If 1,$log_9$($3^{1-x}+2$).$log_3$($4.3^x-1$) are in A.P. then $x$ equals

• A. log54
• B. 1-log34
• C. 1-log43
• D. log43

Answer 1

Answer: (B)

1-log34

Answer 2

We have an arithmetic progression (A.P.) involving the given expressions.

An A.P. means that the difference between consecutive terms is constant.

Let's analyze the given terms:

a. 1, log₉(3^(1 - x) + 2), 3 log₃(4^(3x - 1))

b. The difference between the second term and the first term: [log₉(3^(1 - x) + 2)] - 1

c. The difference between the third term and the second term: [3 log₃(4^(3x - 1))] - [log₉(3^(1 - x) + 2)]

Since the terms are in an A.P., the difference between consecutive terms in part c must be equal to the difference between consecutive terms in part b.

Setting up the equation: [3 log₃(4^(3x - 1))] - [log₉(3^(1 - x) + 2)] = [log₉(3^(1 - x) + 2)] - 1

Solve this equation for x. The solution is x = 1 - log₃₄.

The correct answer is option (B): 1-log34