Question

log2 (8^4)
log (3^5)
solve

Answer 1

Let's solve each expression step by step.

1. **Calculate \(\log_2(8^4)\):**

We can simplify \(8\) as follows:
\[
8 = 2^3
\]
Therefore, we can rewrite \(8^4\) as:
\[
8^4 = (2^3)^4 = 2^{3 \cdot 4} = 2^{12}
\]

Now we can use the properties of logarithms:
\[
\log_2(2^{12}) = 12
\]

So,
\[
\log_2(8^4) = 12
\]

2. **Calculate \(\log(3^5)\):**

We can use the power rule of logarithms, which states that \(\log(a^b) = b \cdot \log(a)\):
\[
\log(3^5) = 5 \cdot \log(3)
\]

Since we don't have values for \(\log(3)\), we can leave the expression as is:
\[
\log(3^5) = 5 \cdot \log(3)
\]

### Final Answers:
- \(\log_2(8^4) = 12\)
- \(\log(3^5) = 5 \cdot \log(3)\)