Question

How do you solve `3^x=729`?

Answer 1

Multiply each side by `log_10` . Eventually, x = 6

Explanation:

Usually, just log means `log_10`, so we can multiply both sides by log.
`log3^x = log 729`
Then, with the log law, we can move the exponent x to the left of log3.
`xlog3 = log729`
Since the x is attached by multiplication, we can divide both sides by log 3.
`x = log(729)/log(3)`
Plug into your calculator and voila!
`x = 6`

I used log since this question was posted in log, but you could also solve by making 729 base 3, then set the exponents equal to each other.
`3^x = 3^6`
`x = 6`
You could also say `x = log_3 (729)` (by using the log function) and plug that into your calculator as well.

Answer 2

`x=6`

Explanation:

We can rewrite `729` as `3^6`. With this in mind, we now have

`3^x=3^6`

Since the bases are the same, we can equate the exponents. We get

`x=6`

Hope this helps!