How do you solve #3^(x-1)=81#?

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Answer 1 · 2016-07-15T08:03:00

#x=5#

As #3^(x-1)=81#, we have

#x-1=log_(3)81=log_(3)3^4#

= #4log_(3)3=4×1=4#

Hence #x=4+1=5#.

Answer 2 · 2016-07-15T09:39:37

#x= 5#

In this example, the fact that #81 # is one of the powers of #3,# allows us to solve this equation using indices. (#3^4 =81#)

If #x^a = x^b " " rArr a = b"#

If the bases are the same then the indices are equal to each other.

#3^(x-1) = 81#
#color(white)(xxxxx)darr#
#color(blue)(3)^color(red)(x-1) = color(blue)(3)^color(red)(4)" the bases are equal"#

#:.color(red)(x-1 = 4)#

#" "x = 5#