exponents!

[cssears]

if 3^x - 3^(x-1) = 162, then x(x-1) =

I broke 162 down into its primes and got 2, 3^4

I figured x(x-1) is really asking what's x^2 - x. so the question is really what is x?

My problem was I couldn't figure out how to solve for x in the equation 3^x - 3^(x-1) = (2)(3^4) (because the of the base 2)

was this the right approach?

Thanks for any insight,
Casey

[mschwrtz]

Basically the right approach....

As a very reliable rule, if you are given an expression of the form

x^a + x^(a+b)

you should rewrite the exponent with the larger power as a multiple of the exponent with the smaller power, so that you get

x^a+(x^b)(x^a)

then factor out the x^a to get

(x^a)[(x^b)+1]

In this problem that means

3^x - 3^(x-1) = 162

3(3^(x-1))-3^(x-1)=162

(3^(x-1))(3-1)=162

3^(x-1)=81

3^(x-1)=3^4

x-1=4

x=5