solve the exponential equation?

e^(x-3) = 1/32
x-3 = ln(1/32)
x = ln(1/32)+3
x = -0.465736

e^(x - 3 ) = 9 / 288 = 1 / 32

( x - 3 ) = ln (1/32)

x = 3 + ln (1/32)

288e^(x - 3) = 9
e^(x - 3) = 9/288
ln[e^(x - 3)] = ln(1/32)
x - 3 = ln(1/32)
x = 3 + ln(1/32)

e^(x - 3) = 9/288

e^(x - 3) = 1/32

(x - 3) ln e = ln (1/32)

x - 3 = ln (1/32)

x = 3 + ln (1/32)

x ≈ -0.466

e^(x-3) = 9/288

e^(x-3) = 1/32

x = ln (1/32) + 3