Question

Logaritmo

Como resolver:
a) Log de 64 na base √2
b) Log de √1/27 na base 3
c) Log de √16 na base 0,25
d) Log de raiz cúbica de 5 na base 125
e) Log de raiz quarta de 32/243 na base 9/4

Answer 1

a)√2 ^x = 64
√2 ^x = 2^6
2^(x/2) = 2^6
x/2=6
x=12
====
b) 3^x=√(1/27)
3^x = (1/27)^1/2
3^x = (1/3³)^1/2
3^x=3^(3/2)
x= 3/2
======
c)0,25^x = √16
0,25^x = 4
(25/100)^x= 4
(1/4)^x=4
4^(-x) = 4
-x=4
x= -4
=======
d)125^x = ∛5
5^3x = 5^(1/3)
3x = 1/3
x = 1/9
========
e)(9/4)^x = (32/243)^(1/4)
3/2^2x = (2/3)^5(1/4)
3/2 ^2x = (2/3)^(5/4)
3/2^2x = 3/2 ^(-5/4)
2x = -5/4
x = -5/8