Respuesta :
Answer:
[tex]logb(X^5 / Y^6)[/tex]
Step-by-step explanation:
Given in the question an expression
5logbX - 6logbY
To Condense the following logs into a single log we will use logarithm rules
1) log power rule
5logbX = logbX^5
6logbY = logbY^6
2)log qoutient rule
ln(x/y) = ln(x)−ln(y)
logbX^5 - logbY^6 = [tex]logb(X^5 / Y^6)[/tex]
Answer:
[tex]5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})[/tex]
Step-by-step explanation:
The given logarithmic expression is [tex]5\log_b(x)-6\log_b(y)[/tex]
We apply the rule: [tex]n\log_b(M)=\log_b(M^n)[/tex]
This implies that;
[tex]5\log_b(x)-6\log_b(y)=\log_b(x^5)-\log_b(y^6)[/tex]
We now apply the rule; [tex]\log_a(M)-\log_a(N)=\log_a(\frac{M}{N} )[/tex]
[tex]5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})[/tex]