To solve this logarithmic expression, we need to use the properties of logarithms.
First, let's rewrite the expression as:
log_0.5(4) + log_5(√25)
Now, let's simplify each logarithm separately.
Using the change of base formula for the first logarithm: log_0.5(4) = log(4) / log(0.5) log_0.5(4) = log(4) / log(1/2) log_0.5(4) = log(4) / (-log(2)) log_0.5(4) = log(4) / (-0.3010) log_0.5(4) ≈ -3.3219
To solve this logarithmic expression, we need to use the properties of logarithms.
First, let's rewrite the expression as:
log_0.5(4) + log_5(√25)
Now, let's simplify each logarithm separately.
Using the change of base formula for the first logarithm:
log_0.5(4) = log(4) / log(0.5)
log_0.5(4) = log(4) / log(1/2)
log_0.5(4) = log(4) / (-log(2))
log_0.5(4) = log(4) / (-0.3010)
log_0.5(4) ≈ -3.3219
Now, simplify the second logarithm:
log_5(√25) = log(√25) / log(5)
log_5(√25) = log(5^(1/2)) / log(5)
log_5(√25) = (1/2)log(5) / log(5)
log_5(√25) = 1/2
Now, add the simplified logarithms back together:
-3.3219 + 1/2
= -3.3219 + 0.5
≈ -2.8219
Therefore, log_0.5(4) + log_5(√25) is approximately equal to -2.8219.