Question

solve the following exponential equations.​

Answer 1

Answer:

See Below

Step-by-step explanation:

(g)

$\\ {5}^{x} = 0.008 \\ \\ {5}^{x} = \frac{8}{1000} \\ \\ {5}^{x} = \frac{1}{125} \\ \\ {5}^{x} = \frac{1}{ {5}^{3} } \\ \\ {5}^{x} = {5}^{ - 3} \\ \\ \huge \red{x = - 3}$

(j)

$\bigg( \frac{1}{3} \bigg)^{3 - x} = \frac{1}{9} \\ \\ \bigg( \frac{1}{3} \bigg)^{3 - x} = \bigg(\frac{1}{3} \bigg)^{2} \\ \\ 3 - x = 2 \\ \\ 3 - 2 = x \\ \\ 1 = x \\ \\ \huge \purple {x = 1} \\ \\

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(m)

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