Question

How do you solve `5^ { 3x } = 1,000`?

Answer 1

Solution: `x ~~ 1.43`

Explanation:

`5^(3 x)= 1000` taking log on both sides we get,

`3 x log (5)= log(1000)` or

`cancel3* x* 0.69897= cancel3`

`x= 1/ 0.69897~~ 1.43 (2 dp)`

Solution: `x ~~ 1.43` [Ans]

Answer 2

Let's solve this problem by converting this into a logarithmic function.

Explanation:

We can first use what I like to call the "swirl rule". This means that in an equation `log_bx=y`, it can rewritten as `b^y=x`. (You can draw a swirling line through each of the variables, hence the name.) This rule also works the other way around. Let's apply this to our equation:

`5^(3x)=1000`
`log_5 1000=3x`

We can then divide each side by 3 to get our answer:

`(log_5 1000)/3=x`
`1.4307~~x`