Exponential Exponent???

Question

Solve for x:

1. (0.04)^x+2 = 256

Note: x+2 is the exponent of 0.04.







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Answer 1

(0.04)^(x + 2) = 256
(x + 2) log (0.04) = log 256
x + 2 = log 256 / log 0.04
x = - 3.72

Note
Any base may be used when taking logs.

Answer 2

You already asked this a few minutes ago:
http://answers.yahoo.com/question/index;_ylt=?qid=20071121005457AADoNBW

To repeat what I said there:

You can try making the bases match on both sides, but in this case it won't work. You need to make use of the fact that log(a^b) = b log(a). Take the log of both sides (it doesn't matter which base). This gets the (x+2) out of the exponent. Then use the properties of logs to simplify.

(0.04)^(x+2) = 256
log [ (0.04)^(x+2) ] = log [256]
(x+2) log (0.04) = log (256)
x+2 = log (256) / log (0.04)
x = [ log (256) / log (0.04) ] - 2
x = [ log (2^8) / log (1/25) ] - 2
x = [ 8 log(2) / log (5^-2) ] - 2
x = [ 8 log (2) / -2 log (5) ] - 2
x = -4 [ log(2) / log(5) ] - 2
x = ( -4 log[base5](2) ) - 2

Answer 3

ln {0.04^(x+2)} = ln256
(x+2)=ln256/ln0.04
x=-3.72