Question

Solve 5^(3x-9)-10=-2

Give the exact solution and an approximate solution to three decimal places.
x = (blank) ≈ (blank)

Answer 1

x = 3.431

Explanation:

Given equation is,

`5^((3x-9))-10=-2`

`5^(3x-9)-10+10=-2+10`

`5^(3x-9)=8`

By taking log on both the sides of the equation,

`\text{log}(5^(3x-9))=\text{log}8`

(3x - 9)log5 = log8

3x - 9 =
`\frac{\text{log}8}{\text{log}5}`

3x - 9 = 1.292

3x = 9 + 1.292

x =
`(10.29202)/(3)`

x = 3.4306

x ≈ 3.431