Posted by **caleb** on Sunday, June 12, 2011 at 9:55pm.

find the exact solution algebraically and check it by substituting into the orginal equation.

1. 36(1/3)^x/5=4

2. 32(1/4)^x/3=2

- pre calc -
**Reiny**, Sunday, June 12, 2011 at 11:44pm
the way you typed it .....

36(1/3)^x = 20

(1/3)^x = .5555555..

x ln(1/3) = .55555..

x = .535 appr.

what you probably meant:

36(1/3)^(x/5) = 4

(1/3)^(x/5) = .111111..

x/5 = ln .111111 / ln(1/3)

x = 10

in the second, you probably have the same typo, and I will assume:

32(1/4)^(x/3) = 2

here is another way to do this:

notice that all factors are powers of 2, so ...

(2^5)(2^-2)^(x/3) = 2^1

2^(-2x/3) = 2^-4

-2x/3 = -4

x = 6

we could have done the first the same way, after dividing both sides by 32 to get

(1/3)^(x/5) = 1/9 = (1/3)^2

so x/5 = 2

x = 10

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