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May 25, 2015

May 25, 2015

Posted by **Caroline** on Friday, April 26, 2013 at 11:57pm.

25. 32^(2x-3)=2

27. 1/4= 2^3x

29. 9^x=27

33. 81^(x-1)= 27^2x

- Pre-Calculus -
**Steve**, Saturday, April 27, 2013 at 5:17amrecall that log(x^a) = a * log x

25)

32^(2x-3) = 2

take log of both sides to get

(2x-3) log 32 = log 2

2x-3 = log 2 / log 32

Now recall that loga/logb = log_b(a)

so, log2/log32 = log_32(2) = 1/5

since 2^5 = 32, 2 = 32^(1/5), so log_32(2) = 1/5

2x-3 = 1/5

2x = 16/5

x = 8/5

Or, we could have started out by noting that 2 = 32^(1/5), so equating powers of 32,

2x-3 = 1/5

...

27)

similarly, since 1/4 = 2^-2,

-2 = 3x

x = -2/3

29)

Since 3= 9^1/2, 27 = 3^3 = 9^3/2, so

x = 3/2

33)

27 = 3^3

81 = 3^4, so

27 = 81^(3/4)

equating powers,

x-1 = 2x(3/4)

x-1 = 3x/2

x/2 = -1

x = -2

check:

81^-3 = 3^-12

27^-6 = 3^-12