Question

СРОЧНО!!! log1/5(x+10)=log3(1/9)

Answer 1

ОДЗ: x + 10 > 0      ⇒  x > - 10
$log _{ \frac{1}{5} }(x+10)=log _{3} \frac{1}{9}\\\\log _{ \frac{1}{5} }(x+10)=-2\\\\x+10=( \frac{1}{5}) ^{-2}\\\\x+10=25\\\\x=15$
Ответ : 15

Answer 2

㏒1/5(х+10)=㏒3(1/9) , х > -10
㏒1/5(х+10)=㏒3(3^-2)
㏒1/5(х+10)=-2
х+10=(1/5)^-2
х+10=5²
х+10=25
х=25-10
х=15 , х > -10
Ответ: х=15

Answer 3

To solve the equation log1/5(x+10) = log3(1/9), we can use the fact that logarithms with different bases can be related to each other using the change of base formula:

loga(x) = logb(x) / logb(a)

Using this formula, we can rewrite the equation as:

log(1/5, x+10) = log(1/9, 3)

log(1/5, x+10) = log(3) / log(1/9)

Now, we can simplify the right-hand side:

log(3) / log(1/9) = log(3) / (log(1) - log(9)) = log(3) / (0 - (-2)) = -log(3) / 2

Substituting this into the equation, we get:

log(1/5, x+10) = -log(3) / 2

To eliminate the logarithm on the left-hand side, we can use the property that loga(b) = c is equivalent to a^c = b:

1/5^(log(1/5, x+10)) = 1/√3

Taking reciprocals and squaring both sides, we get:

5^(log(1/5, x+10)) = 3

Using the change of base formula again, we can rewrite this as:

e^(log(1/5, x+10) * ln(5)) = 3

Taking the natural logarithm of both sides, we get:

log(1/5, x+10) * ln(5) = ln(3)

Solving for log(1/5, x+10), we get:

log(1/5, x+10) = ln(3) / ln(5)

Now, we can use the property that a^log(a, b) = b to eliminate the logarithm on the left-hand side:

1/5^(ln(3) / ln(5)) = x+10

Simplifying, we get:

x + 10 = 3^(ln(5) / ln(3))

x = 3^(ln(5) / ln(3)) - 10

Therefore, the solution to the equation log1/5(x+10) = log3(1/9) is x = 3^(ln(5) / ln(3)) - 10.