Question

(2/3)^x-1=27/8, Find x. Please show a step-by-step explanation.

NB:x is an exponent.


`( (2)/(3) ) {x - 1 = (27)/(8) }^(?)`



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Answer 1

x = -2

`(2/3)^((x-1)) = (27)/(8)`

Explanation:

you have to use logs here

`ln((2/3)^(x) ) =ln(27/8)\\x ln((2/3) ) =ln(275/8)\\\\`

x-1 =ln(27/8)/ ln(2/3)

x -1 = -3

x = -2