Question

Solve for x:

`5^(2x) * 25^3 * 125^2 = (0.04)^-8`

Answer 1

Given expression is `5^(2x) * 25^3 * 125^2 = (0.04)^-8`.

We have to find the value of x in given expression.

Thus, `5^(2x) xx 25^3 xx 125^2 = (0.04)^-8`

`5^(2x) xx (5^2)^3 xx (5^3)^2 = (4/100)^-8`

`5^(2x) xx 5^6 xx 5^6 = (2^2/10^2)^-8`  ...[∴ (aⁿ)^m = a^nm]

`5^(2x + 6 + 6) = (2/10)^(-8 xx 2)` ...[∴ aⁿ × a^m = a^{n + m}]

`5^(2x + 12) = (1/5)^-16`

`5^(2x + 12) = (5^-1)^-16`  ...`[∴ a^-n = 1/a^n]`

`5^(2x + 12) = 5^16`

Equating the powers with same bases.

2x + 12 = 16

2x = 16 – 12

2x = 4

`x = 4/2`

x = 2

Therefore, the value of x in the given expression is 2.