The expression loge(4e3x)log𝑒(4𝑒3𝑥) is equal to
Question
The expression loge(4e3x)log𝑒(4𝑒3𝑥) is equal to
Solution
The expression loge(4e3x) can be simplified using the properties of logarithms.
Step 1: Apply the product rule of logarithms, which states that logb(mn) = logb(m) + logb(n).
loge(4e3x) = loge(4) + loge(e3x)
Step 2: The log base e of e to any power is just that power, so we can simplify loge(e3x) to 3x.
loge(4e3x) = loge(4) + 3x
Step 3: The value of loge(4) is approximately 1.3863.
loge(4e3x) = 1.3863 + 3x
So, the expression loge(4e3x) simplifies to 1.3863 + 3x.
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