Question

help me to solve this problem in copy by finding x

Answer 1

(i)

${2}^{x} + {2}^{x} + {2}^{x} = 192$
192 could also be written as:
${2}^{6} \times 3$
Now, the whole equation becomes
${2}^{x} (1 + 1 + 1) = {2}^{6} \times 3$
${2}^{x} \times 3 = {2}^{6} \times 3 \\ {2}^{x} = {2}^{6}$
As the two bases are same,
therefore,
x= 6.



(ii)
${8}^{255} = {32}^{x}$
8 is equal to 2 raised to thr power 3 and 32 equals 2 raised to the power 5.

So, the given equation becomes
${2}^{(3)(255)} = {2}^{(5)(x)}$
As the two bases are same.
Therefore,
(3)(255)=5x
153 =x.

Hence, in this case x = 153.