Question

Plz i need the answer

Answer 1

x = 96

Explanation:

`log_b \ x = (2)/(3)log_b \ 27 + 3log_b \ 2 - log_b \ 3 + (2)/(3)log_b \ 64 - log_b \ 4`

`=(2)/(3)log_b \ 27 + 3log_b \ 2 + (2)/(3)log_b \ 64 -(log_b \ 3 + log_b \ 4) \\\\=(log_b \ (27)^{(2)/(3)} + log_b \ 2^3 + log_b \ (64)^{(2)/(3)}) -(log_b \ 3 + log_b \ 4) \\\\=log_b \ ( (27)^{(2)/(3)} \cdot 2^3 \cdot (64)^{(2)/(3)}) -log_b \ (3 \cdot 4) \\\\=log_b \ \frac{( (27)^{(2)/(3)} \cdot 2^3 \cdot (64)^{(2)/(3)})}{ (3 \cdot 4)} \\\\=log_b ((9 * 8 * 16)/(3 * 4))\\\\=log_b (3 * 8 * 4)\\\\=log_b \ 96`

Therefore, x = 96