Question

If ,(4/11) to the power x-1=(11/4)to the power 2x-5,
Find the value of x.

Answer 1

Given:

(4/11) to the power x-1=(11/4) to the power 2x-5

To Find:

The value of x.

Solution:

As we know according to the exponential rules,

when the base of the exponents is same then the power is also equal.

Here in this question, we have to make the base same and then compare the powers to find the value of x.

Now,

According to the question:

$(\frac{4}{11}) ^{(x-1)} = (\frac{11}{4} )^{(2x-5)}$

Here the base is not same so we will make the base same by multiplying the power of (11/4) by -1

As  $(a/b)^{2} = (b/a)^{-2}$

So,

$(\frac{4}{11}) ^{(x-1)} = (\frac{4}{11} )^{-(2x-5)}$

$(\frac{4}{11}) ^{(x-1)} = (\frac{4}{11} )^{(5-2x)}$

then,

(x-1) = (5-2x)

x+2x = 5+1

3x = 6

x = 2

Hence,  the value of x is 2.