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#