Question

Jika f(x)=5^3x dan f^-1(x) invers dari f(x) maka nilai f^-1(5 akar5) adalah??

Answer 1

Y = 5^(3x)
3x = 5'log y
x = (5'log y)/3

so, f^-1 (x) = (5'log x)/3
f^-1(5√5) = (5'log 5√5)/3 = (5'log 5^(3/2))/3 = 3/2 * 1/3 * 5'log 5 = 1/2

Answer 2

Y = 5^3x
ubah ke bentuk logaritma
b = a^c ⇔ a'log b = c
maka:
5'log y = 3x
x = (1/3) ⁵log y
f⁻¹ (x) = (1/3) ⁵log x
f⁻¹ (5√5) = (1/3) ⁵log 5√5
= (1/3) ⁵log 5^3/2
= (1/3)(3/2)
= 1/2