Question

Solve each equation. Round to the nearest ten-thousandth.
17(0.3x+5)

Answer 1

first option

Explanation:

using the property of logarithms

ln
`x^(n)` = nlnx ( ln is the natural logarithm )

given

`17^((0.3x+5))` = 12

take the ln of both sides

ln
`17^((0.3x+5))` = ln 12 , then

(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )

0.3x + 5 =
`(ln12)/(ln17)` ≈ 0.877063 ( subtract 5 from both sides )

0.3x ≈ - 4.12293 ( divide both sides by 0.3 )

x =
`(-4.12293)/(0.3)` ≈ - 13.7431 ( to the nearest ten thousandth )