緊急!!F.4 MATHS 求解答,15點!!

Solve the exponential equation 4^x+4^(x－2)=34
Sol
Set y=4^(x－2)
16y=4^x
16y+y=34
y=2
4^(x－2)=2
x－1=1/2
x=5/2

中四好像是在學對數（Logarithm）吧
其實除了兩位的方法外
用log 來 solve 也行的

4^x + 4^(x-2) = 34
(1+1/16)* 4^x = 34
log17 -log16 + xlog4 = log34
x = (log34 - log17 + log16) / log4
x = 2.5

Let y = 4^(x - 2)

4^x = 4^2 * 4^(x - 2) = 16y

So, 4^x + 4^x-2 = 34

16y + y = 34

y = 2

4^(x - 2) = 2

2^[2(x - 2)] = 2

2(x - 2) = 1

x - 2 = 1/2

x = 5/2