Question

3^(x)-3^(x-1)=18,find value of x^x

Answer 1

hey mate

3^(x)-3^(x-1)=18,find value of x^x

answer:

3^(x)-3^(x-1)=18,

3^x(1-1/3)=18

3^x (3-1)/3=18

3^x(2/3)=18

3^x=18×3/2

3^x= 9×3

=3×3×3

3^x = 3³

x= 3.

now,

x^x= 3³

= 27

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Answer 2

We take some help from Laws of Indices

a^(b+c)=a^b.a^c.

so,

3^x-3.^x-3^(-1)

Take 3^x common,3^x(1-3^(-1))

3^-1 is 1/3 or 0.66

3^x(1-1/13)=18

3^x(2/3)=18

3^x=27

Represent 27 as a no of 3's , 27=3*3*3.

3^x=3^3

x=3