The solution to the given logarithmic expressions are;
A) log5(2) = 0.4307
B) log5(75/8) = 1.3906
We are given;
log5(3) = 0.6826
log5(8) = 1.2920
a) To get the value of log5(2);
This can be written as;
Log5 (8)^⅓
From logarithm laws, we know that;
Loga(b)ⁿ = n loga(b)
Thus;
Log5 (8)^⅓ = ⅓log5(8)
>> ⅓ × 1.2920
>> 0.4307
b) For the logarithm function; log5(75/8)
From laws of logarithm, we can express it as;
log5(75/8) = log5(75) - log5(8)
Log5(75) can be written as;
log5(5² × 3)
>> log5(5²) + log5(3)
Thus;
log5(75/8) = log5(5²) + log5(3) - log5(8)
>> 2log5(5) + log5(3) - log5(8)
>> 2(1) + 0.6826 - 1.2920
>> 1.3906
Read more about logarithmic expressions at; https://brainly.com/question/25790056
