Question

Solve the following exponential equations.​

Answer 1

See Below

Explanation:

(g)

`\\ {5}^(x) = 0.008 \\ \\ {5}^(x) = (8)/(1000) \\ \\ {5}^(x) = (1)/(125) \\ \\ {5}^(x) = \frac{1}{ {5}^(3) } \\ \\ {5}^(x) = {5}^( - 3) \\ \\ \huge \red{x = - 3} \\ \\`

(j)

`\bigg( (1)/(3) \bigg)^(3 - x) = (1)/(9) \\ \\ \bigg( (1)/(3) \bigg)^(3 - x) = \bigg((1)/(3) \bigg)^(2) \\ \\ 3 - x = 2 \\ \\ 3 - 2 = x \\ \\ 1 = x \\ \\ \huge \purple {x = 1} \\ \\</p><p>`

(m)

`\bigg( \sqrt{ (5)/(7) } \bigg)^(x - 1) = \bigg( (125)/(343) \bigg)^( - 1) \\ \\ \bigg( { (5)/(7) } \bigg)^{ (x - 1)/(2) } = \bigg( (5)/(7) \bigg)^( - 3) \\ \\ (x - 1)/(2) = - 3 \\ \\ x - 1 = - 6 \\ \\ x = - 6 + 1 \\ \\ \huge \orange{ x = - 5}`