Question

write in simplest form 4log(B) 6 +log(b) 4

Answer 1

To simplify the expression \( 4 \log(B) 6 + \log(B) 4 \), we can use the properties of logarithms.

1. Start with the expression:
\[
4 \log(B) 6 + \log(B) 4
\]

2. The first term, \( 4 \log(B) 6 \), can be rewritten using the power rule of logarithms:
\[
4 \log(B) 6 = \log(B) 6^4 = \log(B) 1296
\]

3. Now, we can rewrite the entire expression:
\[
\log(B) 1296 + \log(B) 4
\]

4. Using the property that \( \log(a) + \log(b) = \log(ab) \), combine the two logarithms:
\[
\log(B) 1296 + \log(B) 4 = \log(B) (1296 \times 4)
\]

5. Calculate \( 1296 \times 4 \):
\[
1296 \times 4 = 5184
\]

6. Therefore, we can write:
\[
\log(B) 1296 + \log(B) 4 = \log(B) 5184
\]

In simplest form, the expression \( 4 \log(B) 6 + \log(B) 4 \) is:
\[
\log(B) 5184
\]