+0

# help

0
53
1

Compute  $$\large 81^{1/\log_5 3} + 27^{\log_9 36} + 3^{4 /\log_7 9}$$

Jun 18, 2020

### 1+0 Answers

#1
+8336
0

Notice that $$\dfrac1{\log_ab} = \log_ba$$ and $$c^{\log_c a} = a$$.

We will call the first equation (1) and the second equation (2).

$$\quad 81^{1/\log_53} + 27^{\log_936}+3^{4/\log_79}\\ \stackrel{(1)}{=} 3^{4\log_35} + 9^{1.5\log_936} + 9^{2\log_97}\\ \stackrel{(2)}{=} 5^4 + 36^{1.5} + 7^2$$

The rest is simple.

Jun 18, 2020