Question

Уравнение: log3x+2 logx3 = 3.​

Answer 1

log3 x=1/ logx 3  

обозначим log3 x=y  

y+2/y=3  

(y²+2)/y=3  

y²-3y+2=0  

y1-2=(3+-√(9-8))/2=(3+-1)/2={1;2)  

1) log3 x=1  

x=3  

2) log3 x=2  

x=3²=9  

Пошаговое объяснение:

Answer 2

To solve the equation log3(x) + 2logx(3) = 3, we'll use logarithm properties to simplify it first and then find the value of x.

Logarithm properties used:

1. log(a) + log(b) = log(a * b)
2. log(a^n) = n * log(a)

Given equation: log3(x) + 2logx(3) = 3

Using property 2, we can rewrite 2logx(3) as logx(3^2) or logx(9):

log3(x) + logx(9) = 3

Now, we can combine the logarithms using property 1:

log3(x * 9) = 3

Simplify further:

log3(9x) = 3

Now, we can convert the logarithmic equation into an exponential equation:

3^3 = 9x

27 = 9x

Finally, solve for x:

x = 27 / 9

x = 3

So, the solution to the equation is x = 3.