Question

A) log2 32 - log2 4= 5-4 =1 b) 2 = c) 3log4 2 + log4 8=

Answer 1

С) log4 2^3+log4 8=log4 8+log4 8=log4 8*8=log4 64=3

Answer 2

A) log2 32 - log2 4 = 5 - 4 = 1

To solve this equation, let's simplify each side step by step.

First, let's simplify the left side of the equation using the logarithmic properties. According to the logarithmic property log_a b - log_a c = log_a (b/c), we can rewrite the equation as:

log2 32 - log2 4 = log2 (32/4)

Now, we can simplify the expression inside the logarithm:

32/4 = 8

So the equation becomes:

log2 (8) = 1

The logarithm base 2 of 8 equals 1. This means that 2 raised to the power of 1 gives us 8. Therefore, the equation is true.

B) 2^3 = ?

To solve this equation, we need to evaluate 2 raised to the power of 3.

2^3 means 2 multiplied by itself 3 times:

2^3 = 2 * 2 * 2 = 8

So, 2^3 is equal to 8.

C) 3log4 2 + log4 8 = ?

To solve this equation, we can use the logarithmic properties to simplify the expression.

Using the logarithmic property log_a b^n = n * log_a b, we can rewrite the equation as:

3log4 2 + log4 8 = log4 (2^3) + log4 8

Simplifying further, we get:

log4 (8) + log4 8

Now, using the logarithmic property log_a b + log_a c = log_a (b * c), we can combine the two logarithms:

log4 (8 * 8)

Simplifying the expression inside the logarithm:

8 * 8 = 64

So the equation becomes:

log4 (64)

Since 4 raised to the power of what gives us 64? The answer is 3.

Therefore, the equation is:

log4 (64) = 3.