qual a soma de log de 1/25 base 1/5 - log de 7 base 1/49 - log de raiz de 32 base 4
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log(1/5) 1/25 = x
1/5 = 5^ -1
1/25 = 5^ -2
log(5^-1) 5^ -2 = x
(5^ -1)^x = 5^-2
5 ^ -x = 5 ^ -2
-x = -2
x = 2
log(1/49) 7 = y
1/49 = 7^ -2
log(7^ -2) 7 = y
(7^ -2)^y = 7
7 ^ -2y = 7^1
-2y = 1
y = -1/2
log(4) raiz de 32 = z
4 = 2²
raiz de 32 = raiz de 2^5 = 2^ 5/2
log(2²) 2^ 5/2 = z
2²^ z = 2^ 5/2
2^2z = 2^5/2
2z = 5/2
z = 5/4
x - y - z = 2 - (-1/2) - 5/4 = 2 + 1/2 - 5/4 = 5/2 - 5/4 = 5/4
1/5 = 5^ -1
1/25 = 5^ -2
log(5^-1) 5^ -2 = x
(5^ -1)^x = 5^-2
5 ^ -x = 5 ^ -2
-x = -2
x = 2
log(1/49) 7 = y
1/49 = 7^ -2
log(7^ -2) 7 = y
(7^ -2)^y = 7
7 ^ -2y = 7^1
-2y = 1
y = -1/2
log(4) raiz de 32 = z
4 = 2²
raiz de 32 = raiz de 2^5 = 2^ 5/2
log(2²) 2^ 5/2 = z
2²^ z = 2^ 5/2
2^2z = 2^5/2
2z = 5/2
z = 5/4
x - y - z = 2 - (-1/2) - 5/4 = 2 + 1/2 - 5/4 = 5/2 - 5/4 = 5/4
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