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Given that the solution of the equation 2x + a = X-6 is x = 6, who will find the value of 3a-9?
Taking x = 6 into 2x + a = X-6, we can get a = - 12, so 3a-9 = 3 × (- 12) - 9 = - 45
Exponential and logarithmic equations
X1 is the root of the equation xlgx = 2007, X2 is the root of the equation x10x = 2007, find x1x2
Solution
For the convenience of writing, I use a and B instead of X1 and x2
∵alga=2007,b10^b=2007
Then LG (alga = 2007) = LGA + lglga = lg2007 ①
lglg(b10^b)=lgb+lglgb=lglg2007 ②
① It is easy to get that the function y = lgx is monotone
∴ab·lgab=2007lg2007,
And the function y = xlgx is a monotone function, х AB = 2007
Solving logarithmic equation
Solve the equation LG (x ^ 2 + 11x + 8) = LG (x + 1) = 1
There must be a process of answer and the final conclusion answer, clear answer to the additional bonus!
I guess the original equation is LG (x ^ 2 + 11x + 8) - LG (x + 1) = 1
lg(x^2+11x+8)-lg(x+1)=1
lg[(x^2+11x+8)/(x+1)]=lg10
(x^2+11x+8)/(x+1)=10
x^2+11x+8=10(x+1)
x^2+x-2=0
(x+2)(x-1)=0
x1=-2,x2=1
To make the original equation meaningful, x ^ 2 + 11x + 8 > 0, x + 1 > 0
We get x > (- 11 + √ 89) / 2
Then X1 = - 2 is omitted
The solution of the original equation is x = 1
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