For a real number x 1, the value of 1/log_2(x) + 1/log_3(x) + 1/log_4(x) = 1. The value of x is

A. 4
B. 12
C. 24
D. 3...

Question

For a real number x > 1, the value of 1/log_2(x) + 1/log_3(x) + 1/log_4(x) = 1. The value of x is

A. 4
B. 12
C. 24
D. 36

Accepted Answer

x = 24 The reciprocal identity 1/log_b(x) = log_x(b) converts each term to a base-x logarithm. The three terms become log_x(2) + log_x(3) + log_x(4), which the product rule collapses to log_x(24). Setting log_x(24) = 1 means x^1 = 24, so x = 24.

For a real number x > 1, the value of 1/log_2(x) + 1/log_3(x) + 1/log_4(x) = 1. The value of x is A. 4 B. 12 C. 24 D. 36