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(2006•静安区二模)方程log4(2x+10)=log4(x+3)+log4(3-x)的解x=______.

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解题思路:利用对数的运算性质及对数的定义域即可求得答案.

∵log4(2x+10)=log4(x+3)+log4(3-x)


2x+10>0
x+3>0
3−x>0
2x+10=(x+3)(3−x)①解①得x=-1,经检验,满足题意,
∴方程log4(2x+10)=log4(x+3)+log4(3-x)的解x=-1.
故答案为:-1.

点评:
本题考点: 函数的零点.

考点点评: 本题考查函数的零点,着重考查对数方程的解法,考查方程思想与运算能力,属于中档题.

1年前

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