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

Aug 3, 2016

$27 = {3}^{x}$

#### Explanation:

Using the $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}} \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\log}_{b} a = n \Leftrightarrow a = {b}^{n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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

$\Rightarrow 27 = {3}^{x} \text{ in exponential form}$

By the way, $x = 3 \text{ since} 27 = {3}^{3}$

Aug 3, 2016

$x = 3$

#### Explanation:

When we write ${\log}_{a} C = b$, we ask to what power we raise the base, $a$, to get $C$; since ${\log}_{a} C = b$, 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 ${3}^{3}$ $=$ $3 \times 3 \times 3 = 27$, ${\log}_{3} 27 = 3$