Question

How do you write `log_3 27=x` in exponential form?

Answer 1

`27=3^x`

Explanation:

Using the `color(blue)"law of logarithms"`

`color(orange)"Reminder" color(red)(|bar(ul(color(white)(a/a)color(black)(log_b a=nhArra=b^n)color(white)(a/a)|)))`

here a = 27 , b = 3 and n = x

`rArr27=3^x" in exponential form"`

By the way, `x=3" since" 27=3^3`

Answer 2

`x=3`

Explanation:

When we write `log_aC=b`, we ask to what power we raise the base, `a`, to get `C`; since `log_aC=b`, then, by definition of the logartihmic function, `a^b=C`.

In your problem, we want to find `log_(3)27`, in other words we want to find the power to which we raise `3` to get `27`.

Since `3^3` `=` `3xx3xx3=27`, `log_(3)27=3`