To solve this logarithmic expression, we will use the properties of logarithms.
Logarithm properties:
Given expressionlog12 9 + 2 log12 4
Using the third logarithmic property, we can rewrite log12 4 as log12 4^2:
log12 9 + log12 (4^2)
Now, using the first logarithmic property, we can combine the two logarithms:
log12 (9 * 4^2)
Simplifying the expression inside the logarithm:
log12 (9 * 16)
log12 144
Therefore, the final simplified expression is log12 144.
To solve this logarithmic expression, we will use the properties of logarithms.
Logarithm properties:
log(a) + log(b) = log(ab)log(a) - log(b) = log(a/b)log(a)^b = b * log(a)Given expression
log12 9 + 2 log12 4
Using the third logarithmic property, we can rewrite log12 4 as log12 4^2:
log12 9 + log12 (4^2)
Now, using the first logarithmic property, we can combine the two logarithms:
log12 (9 * 4^2)
Simplifying the expression inside the logarithm:
log12 (9 * 16)
log12 144
Therefore, the final simplified expression is log12 144.