How does logX X prove it? logex equals lnx what

Convention: [ Inner logarithm.

Base. The original question is: log[2]x0).

All you need is (ln2)x-lnx>0 (x>0) and f(x)=(ln2)x-lnx

f'(x)=(ln2)-(1/x )=(x-(1/ln2))(ln2/x) (x>0)

x ∈(0,1/ln2),f'(x) <0 and f(x) on it.

minus, x (1 ln2, + f'(x) >0 and f(x) increment on it.

f'(1 ln2)=0, f(x) takes the minimum value at x=1 ln2 and the minimum value f(1 ln2)=1+ln(ln2)).

And 1+ln(ln2))>1+ln(1 e))=0 gets (ln2)x-lnx f(1 ln2)>0, so log[2]x hope it helps you!

y=x;y=log2x is a picture of these two figures.

Solution: log[2]x0).

All you need is (ln2)x-lnx>0 (x>0) and f(x)=(ln2)x-lnx

f'(x)=(ln2)-(1/x )=(x-(1/ln2))(ln2/x) (x>0)

x ∈(0,1/ln2),f'(x) <0, f(x) on which it is single minus, x (1 ln2, + f.)'(x) >0 and f(x) increment on it.

f'(1 ln2)=0, f(x) takes the minimum value at x=1 ln2 and the minimum value f(1 ln2)=1+ln(ln2)).

And 1+ln(ln2))>1+ln(1 e)))=0 gives (ln2)x-lnx f(1 ln2)>0, so log[2]x

logex is equal to lnx. Analysis: LNX is the logarithm of loge x.

Logarithmic arithmetic:1、log(a) (m·n）=log(a) m+log(a) n2、log(a) (m÷n)=log(a) m-log(a) n3、log(a) m^n=nlog(a) m4、log(a)b*log(b)a=1

5. log(a) b=log(c) b log(c) a

1. [a m] [a n]=a (m n) [same base.]

Multiply the power, the base number does not change, and it refers to the addition of the quiet number].

2. [a m] [a n]=a (m n) [divide by the power of the same base, the base does not change, and the exponent subtracts the prudent].

3. [a m] n=a (mn) [the power of the power, the base is unchanged, the exponents are multiplied] 4. [ab] m=(a m) (a m) [the power of the product, equal to each factor.

Multiply the square separately, and then multiply the power obtained by Min Jing].

logex is equal to lnx.

The analysis is as follows: lnx is the logarithm of loge x, and logex is equal to lnx.

Logarithmic arithmetic:

1、log(a) (m·n）=log(a) m+log(a) n

2、log(a) (m÷n)=log(a) m-log(a) n

3、log(a) m^n=nlog(a) m

4、log(a)b*log(b)a=1

5、log(a) b=log (c) b÷log (c) a

Algorithm of Exponents:

1. [a m] [a n]=a (m n) [multiply with the power of the base, the base does not change, and the exponent is added].

2. [a m] [a n]=a (m n) [divide carefully by the power of the same base, the base remains unchanged, and the exponent is subtracted].

3. [a m] n=a (mn) [power of power, base unchanged, exponential multiplication].

4. [ab] m=(a m) (a m) [the power of the product is equal to the multiplication of each factor, and then multiply the power obtained by Jan Minjing].