Question

A)Log6 144-Log6 4 B)Log4 32+2Log4 √2

Answer 1

А) log6 144/4=log6 36=2
Б) log4 32*2=log4 64=3

Answer 2

To simplify the given expressions, we'll use some logarithmic properties. The two properties we'll be using are:

1. log_b(xy) = log_b(x) + log_b(y)
2. log_b(x^y) = y * log_b(x)

Let's simplify each expression:

A) Log6 144 - Log6 4

We can use the first logarithmic property to combine the two logarithms:

Log6 144 - Log6 4 = Log6 (144/4) = Log6 36

Now, we need to find the value of log base 6 for 36. In other words, we need to find "x" in the equation 6^x = 36.

6^2 = 36

So, Log6 36 = 2

Therefore, the value of A) Log6 144 - Log6 4 is 2.

B) Log4 32 + 2Log4 √2

First, we can use the second logarithmic property to simplify the second term:

2Log4 √2 = Log4 (√2)^2 = Log4 2

Now, we have:

Log4 32 + 2Log4 √2 = Log4 (32) + Log4 2

We can further simplify the first term using logarithmic property 1:

Log4 32 = Log4 (2^5) = 5

So, the expression becomes:

Log4 32 + Log4 2 = 5 + Log4 2

Therefore, the value of B) Log4 32 + 2Log4 √2 is 5 + Log4 2.