Question

`5^(3x)-5^(3x-1)=4` In the following equation, solve for x (to two decimal places if necessary) and write all the steps until the final answer.

Answer 1

`x = (1)/(3)`

or x = 0.33

Explanation:

`{5}^(3x) - {5}^(3x - 1) = 4 \\ \\ \implies{5}^(3x) - {5}^(3x) . {5}^( - 1) = 4 \\ \\ \implies{5}^(3x)(1 - {5}^( - 1) )= 4 \\ \\ \implies{5}^(3x) \bigg(1 - (1)/(5) \bigg)= 4 \\ \\ \implies{5}^(3x) \bigg((5 - 1)/(5) \bigg)= 4 \\ \\ \implies{5}^(3x) * (4)/(5) = 4 \\ \\ \implies{5}^(3x) = 4 *(5)/(4) \\ \\ \implies{5}^(3x) =5 \\ \\ \implies \: 3x = 1 \\ \\ \huge \implies \: x = (1)/(3) \\\\ \huge \implies \: x = 0.33`