Question

Condense the following logs into a single log:

$5log_{b} x - 6log_{b} y$

Answer 1

Answer:

$logb(X^5 / Y^6)$

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 = $logb(X^5 / Y^6)$

Answer 2

Answer:

$5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})$

Step-by-step explanation:

The given logarithmic expression is  $5\log_b(x)-6\log_b(y)$

We apply the rule: $n\log_b(M)=\log_b(M^n)$

This implies that;

$5\log_b(x)-6\log_b(y)=\log_b(x^5)-\log_b(y^6)$

We now apply the rule; $\log_a(M)-\log_a(N)=\log_a(\frac{M}{N} )$

$5\log_b(x)-6\log_b(y)=\log_b(\frac{x^5}{y^6})$