Question

if 3 by 8 power minus 5 x 16 by 21 power minus 5 is equals to 2 by 7 power x find x square ​

Answer 1

Step-by-step explanation:

question can be written as:

{(3/8)^-5}×{(16/21)^-5}=(2/7)^x

={(8/3)^5}×{(21/16)^5}=(2/7)^x

={(4×2)/3}^5×{(7×3)/(4×4)}^5=(2/7)^x

=2^5×(7/4)^5=(2/7)^x, [4^5 cancel out 1/4^5 and 3^5 cancel out 1/3^5]

=(2^5×7^5)/4^5=(2/7)^x

=(2^5×7^5)/2^5×2^5=(2/7)^x

=7^5/2^5=(2/7)^x

therefore,we can write it as,

2^-5/7^-5=(2/7)^x

(2/7)^-5=(2/7)^x

therefore,X=-5.