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]

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