Question

I need help!!

Use the properties of logarithms to simplify.

log base5 5^(2x − 9) + log base3 729^5

Answer 1

2x +21

Explanation:

`log_(5) {5}^((2x - 9)) + log_(3) {729}^(5) \\ \\ = log_(5) {5}^((2x - 9)) + log_(3) {( {3}^(6) )}^(5) \\ \\ = log_(5) {5}^((2x - 9)) + log_(3) { {3}}^(6 * 5) \\ \\ = log_(5) {5}^((2x - 9)) + log_(3) { {3}}^(30) \\ \\ =(2x - 9) log_(5) {5} + 30 log_(3) { {3}} \\ \\ = (2x - 9).1 + 30(1 )\\ ( \because \: log_(a) { {a}} = 1) \\ \\ = 2x - 9 + 30 \\ \\ = 2x +21`