Question

2log x / log(5x-4)= 1​

Answer 1

Answer:

x = 4

Note:

★ log(A•B) = logA + logB

★ log(A/B) = logA - logB

★ logAⁿ = n(logA)

★ log1 = 0

★ logA = logB => A = B

Solution:

We have ;

=> 2logx / log(5x - 4) = 1

=> 2logx = log(5x - 4)

=> logx² = log(5x - 4)

=> x² = 5x - 4

=> x² - 5x + 4 = 0

=> x² - 4x - x + 4 = 0

=> x(x - 4) - (x - 4) = 0

=> (x - 4)(x - 1) = 0

=> x = 1 , 4

Also,

At x = 1

log(5x - 4) = log(5×1 - 4)

= log(5 - 4)

= log1

= 0

Here ,

x = 1 is rejected value , because at x = 1 the value of log(5x - 4) is 0 which is not possible to have in denominator .

Thus,

The appropriate value of x is 4 .

Hence,

x = 4