Question

the solution to log6(x+4/x-1)=1​

Answer 1

Required Answer:-

Given:

• $\sf \log_{6} \bigg( \dfrac{x + 4}{x - 1}\bigg) = 1$

To Find:

• The value of x.

Solution:

We have,

$\sf \implies \log_{6} \bigg( \dfrac{x + 4}{x - 1}\bigg) = 1$

We know that,

$\sf \log_{x}(y) = z \implies {x}^{z} = y$

Therefore,

$\sf \implies \bigg( \dfrac{x + 4}{x - 1}\bigg) = {6}^{1}$

On cross multiplying,

$\sf \implies x + 4 = 6(x - 1)$

$\sf \implies x + 4 = 6x - 6$

$\sf \implies 5x = 10$

$\sf \implies x = 2$

★ Hence, the value of x satisfying the equation is 2.

Answer:

• The value of x satisfying the equation is 2.

Verification:

Let us verify our result.

Plugging the value of x, we get,

$\sf \log_{6} \bigg( \dfrac{x + 4}{x - 1}\bigg)$

$\sf = \log_{6} \bigg( \dfrac{2+ 4}{2 - 1}\bigg)$

$\sf = \log_{6} \bigg( \dfrac{6}{1}\bigg)$

$\sf = \log_{6}(6)$

$\sf = 1$

Hence, our answer is correct (Verified)