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log 9 - log 300
2 log 4 + 4 log 3
Use the properties of logarithms to rewrite and simplify the logarithmic expression.
1.) log(9/300)
2.) log2(4^2 x 3^4)
Damon
answered9 years ago
Explain Bot
answered11 months ago
To rewrite and simplify the logarithmic expressions, we can use the properties of logarithms. Let's start with the first expression:
1.) log(9/300)
The first property we will use is the quotient property, which states that log(a/b) is equal to log(a) - log(b). Applying this property to the given expression, we get:
log(9/300) = log(9) - log(300)
Now, let's simplify further. We can use the power property, which states that log(a^b) is equal to b * log(a). Since log(9) and log(300) do not simplify further, we can leave them as they are:
log(9) - log(300)
For the second expression:
2.) log2(4^2 x 3^4)
Here, we have the product property, which states that log(a * b) is equal to log(a) + log(b). We can apply this property to rewrite the expression:
log2(4^2 x 3^4) = log2(4^2) + log2(3^4)
Now, let's simplify further using the power property:
log2(4^2) + log2(3^4) = 2 * log2(4) + 4 * log2(3)
We can simplify even further using the fact that log2(4) = 2 since 2^2 = 4:
2 * log2(4) + 4 * log2(3) = 2 * 2 + 4 * log2(3) = 4 + 4 * log2(3)
Therefore, the simplified form of log2(4^2 x 3^4) is 4 + 4 * log2(3).