Question

Log^2(x-5)+log^2(x+2)=log^2 18

Answer 1

Ответ:

х=7

Пошаговое объяснение:

log^2(x-5)+log^2(x+2)=log^2 18 х∈(5,+∞)

log^2((x-5)*(x+2))=log^2 18

log^2(х2+2х-5х-10)=log^2 18

х2+2х-5х-10=18

х2-3х-10=18

х2-3х-10-18=0

х2-3х-28=0

х=3+-√9+112/2

х=3+-11/2

х=3+11/2

х=3-11/2

х=7

х=-4

х∈(5,+∞)

х=7

/- черта дроби

Answer 2

It seems like you have an equation involving logarithms that you would like to solve. To make it easier to read, I'll rewrite it as follows:

$\log^2(x - 5) + \log^2(x + 2) = \log^2 18$

Let's work on solving this equation step by step:

Step 1: Simplify the equation using logarithmic properties $\log^2(x - 5) + \log^2(x + 2) = \log^2 18$

Since the equation involves squared logarithms, we can rewrite it as: $(\log(x - 5))^2 + (\log(x + 2))^2 = (\log 18)^2$

Step 2: Apply the property $(\log a)^2 = \log a \times \log a$: $\log(x - 5) \times \log(x - 5) + \log(x + 2) \times \log(x + 2) = (\log 18)^2$

Step 3: Use the property $\log a + \log b = \log(ab)$: $\log[(x - 5)(x + 2)] = (\log 18)^2$

Step 4: Convert the equation back to an exponential form: $(x - 5)(x + 2) = 18^{(\log 18)^2}$

Step 5: Solve for x: $x^2 - 3x - 8 = 18^{(\log 18)^2}$

This is a quadratic equation. We can solve it by setting it equal to zero and then applying the quadratic formula, but it's important to note that the right-hand side contains a constant raised to the power of another constant, which will yield a specific value. However, without knowing the value of $\log 18$, we won't be able to get an exact numerical solution.

If you have a specific value for $\log 18$, you can substitute it into the equation and proceed to solve for $x$. Otherwise, you will need to provide additional information or constraints to get a more precise answer.