Help me

1.Solve the following equations.
2^2x - 7(2x) - 8 = 0
2^2x - 7(2x) - 8 = 0
2^x+x - 7(2x) - 8 = 0
(2x)(2x) - 7(2x) - 8 = 0
(2x)² - 7(2x) - 8 = 0
(2x - 8)(2x + 1) = 0
2x - 8 = 0 or 2x + 1 = 0
2x = 8 or 2x = -1 (rejected as 2x >= 0)
2x = 2³
xlog2 = 3log2
x = 3
So x = 3.
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2.Let f(x) = 14 + x15
Hence find the remainder when 14 + 1615 is divided by 17.
題目好似未完整，你意思是否指（希望我的理解沒錯）：
Let f(x) = 14 + x15, find the remainder when f(x) is divided by x+1
Hence find the remainder when 14 + 1615 is divided by 17.
By remainder theorem,
When f(x) is divided by x-n, the remainder is f(n). So
the remainder when f(x) is divided by x+1
= f(-1)
= 14 + (1)15
= 14 + 1
= 15
The remainder when f(x) = 14 + x15 is divided by x+1 is 15 .... (*)
14 + 1615 = f(16)
So substitute x=16 into (*), we have
The remainder when f(16) = 14 + 1615 is divided by 16+1=17 is 15.

2006-12-14 17:18:32 補充：
小小補充：常應用到的 log 公式有：log(a^b) = b logalog(ab) = loga + logblog(a/b) = loga - logblog[(a^(bc)] = [log(a^b)]^c