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

2 Answers
Aug 3, 2016

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

Aug 3, 2016

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