Question

Log_4 8+log_4 2+log_4 8+log_4 8

Answer 1

log₄8+log₄2+log₄8+log₄8= log₄8×2 + log₄8×8= log₄16+log₄64= 2+3= 5.

По формуле логарифма произведения чисел...

Answer 2

Let's simplify the expression step by step using logarithmic properties. Remember that in logarithms, the base of the logarithm indicates what you're taking the logarithm of.

1. Logarithmic Addition Rule: log_a(b) + log_a(c) = log_a(b * c)

Using this property, we can simplify the given expression:

log_4(8) + log_4(2) + log_4(8) + log_4(8)

Now, apply the addition rule:

log_4(8 * 2 * 8 * 8)

2. Simplify the Multiplication:

8 * 2 * 8 * 8 = 1024

So, the expression becomes:

log_4(1024)

3. Logarithmic Power Rule: log_a(b^c) = c * log_a(b)

Apply the power rule:

log_4(4^5)

4. Simplify the Power:

4^5 = 1024

So, the expression becomes:

log_4(1024) = 5

Therefore, the simplified value of the expression is 5.