Question

Решить систему 3,9, 1/5 - основание логарифма

Answer 1

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Answer 2

Log(3)x+log(9)y=3
log(9)y=3-log(3)x
log(3)y/2=3-log(3)x
log(3)y=6-2log(3)x
Подставим во 2
log(1/5)x+log(3)y=3
log(1/5)x+6-2log(3)x=3
-log(3)x/log(3)5 -2log(3)x+3=0
-log(3)x-2log(5)3*log(3)x+3log(3)5=0
-log(3)x *(1+2log(3)5)=-3log(3)5
log(3)x=3log(3)5/(1+2log(3)5) 
log(3)x=  log(3)125/log(3)75=log(75)125
x=3^log(75)125 

Answer 3

Solving the Logarithmic Equation

To solve the logarithmic equation 3,9 = 1/5 + log(base) x, we can use the properties of logarithms to isolate the variable x.

First, let's rewrite the equation in exponential form. The logarithmic equation 3,9 = 1/5 + log(base) x can be expressed as:

x = base^(3,9 - 1/5)

Now, we can calculate the value of x using the given base and the logarithmic value.

Calculating the value of x: x = base^(3,9 - 1/5)

This will give us the solution for the given logarithmic equation.

Let's proceed with the calculation.