Question

Lgx=1/2lg-3lg b+5lg c log3x=log3 2+log9 3 lgx=log10x^2+log100 121 Log ax=3loga 7-0,25 loga3

Answer 1

1) по свойству логарифма  

log8(x^2-1)=1  

x^2-1=8^1  

x^2-1=8  

x^2=9  

x=3 и x=-3  

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2)  

log2(5x-x2)=2  

5х-x^2=4  

x^2-5x+4=0  

x=1 и x=4  

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3)lg^2x-5lgx+6=0  

lg(x)=y  

y^2-5y+6=0  

y=2 => lgx=2 =>x=100  

y=3=>lgx=3=>x=1000  

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4)  

log3(x-2)+log3(x-4)=1  

log3[(x-2)*(x-4)]=1  

(x-2)*(x-4)=3  

x^2-6x+8=3  

x^2-6x+5=0  

x=5  

x=1  

 

Вот и все

Answer 2

Let's simplify each of the logarithmic expressions step by step:

1. Lgx = 1/2lg(-3lg(b)) + 5lg(c) Note: I assume "lg" refers to the logarithm base 10 (common logarithm).

   We can use the logarithm property: lg(a) + lg(b) = lg(a * b) Lgx = 1/2 * lg((-3) * lg(b)) + 5 * lg(c)

   Now, another property: lg(a^b) = b * lg(a) Lgx = 1/2 * (-3 * lg(b)) + 5 * lg(c)

   Finally, lg(10) = 1, so we can simplify further: Lgx = -3/2 * lg(b) + 5 * lg(c)

2. log3(x) = log3(2) + log9(3) Note: I assume the logarithm is base 10, unless otherwise specified.

   We can use the change of base formula: loga(b) = logc(b) / logc(a) log3(x) = log(x) / log(3) + log(3) / log(9)

   Now, recall that log(9) = 2 because 3^2 = 9: log3(x) = log(x) / log(3) + log(3) / 2

3. lgx = log10(x^2) + log100(121) Here, I'll assume the logarithms are base 10.

   We can simplify using properties: lg(x) = 2 * log(x) + 2 * log(11)

4. Log(ax) = 3log(a, 7) - 0.25log(a, 3) Here, I'll assume the logarithms are base 10.

   We can use properties of logarithms: Log(ax) = log(a, 7^3) - log(a, 3^(1/4))

   Now, 7^3 = 343 and 3^(1/4) is the fourth root of 3: Log(ax) = log(a, 343) - log(a, 3^(1/4))

   Finally, we know that log(a, a) = 1 for any base a, so: Log(ax) = 3 - (1/4) * log(a, 3)

Please note that some expressions may have different bases for logarithms or missing information. If you can provide more context or clarification, I can assist you further with the specific problem.