Question

Ques. 18^(4X - 3) = (54√2)^(3x-4), then x is equal to:

a. 6
b. 8
c.4
d. 10
​

Answer 1

Answer:

a. 6.

Step-by-step explanation:

$18^{4x - 3} = (54\sqrt{2})^{3x - 4}$

$18^{4x - 3} = (18^\frac{3}{2})^{3x - 4}$

$18^{4x - 3} = (18)^{\frac{9x - 12}{2}$

Now, $4x - 3 = \frac{9x - 12}{2}$

So, $8x - 6 = 9x - 12$

$x = 6$

Answer 2

Answer:

The value of $x=6$.

Step-by-step explanation:

$(18)^{4x-3} = (54\sqrt{2} )^{3x-4}$

$(18)^{4x-3} = (18^{\frac{3}{2} } )^{3x-4}$

$(18)^{4x-3} = (18)^{\frac{9x-12}{2} }$

Here, comparing the powers of the terms in LHS and RHS,

$4x-3 = \frac{9x-12}{2}$

Bringing the $2$ to LHS,

$8x-6=9x-12$

$-6+12=9x-8x$

$6=x$

Hence we get that the value of $x=6$