Question

How do you solve `log_x729=6`?

Answer 1

By trying random numbers, 3 is obviously correct. However, if the answer was not an integral, the root function has to be derived and used (through calculator).

Explanation:

We can apply the logarithmic property:

`a=log_x(x^a)`

`log_x729=log_x(x^6)`

Since `logx` is a 1-1 function for any `x>0` and `x!=1` , the logarithms can be ruled out:

`729=x^6`
`729^(1/6)=(x^6)^(1/6)`
`x=729^(1/6)=root(6)(729)=3`