Question

Log5 log3 log2 (x^2+7x)=0 помогите плииз

Answer 1

Log3 log2 (x^2+7x)=1
log2 (x^2+7x)=3
x^2+7x-8=0
D=49+32=81
x1=1
x2=-8

Answer 2

Solving the Equation log5(log3(log2(x^2+7x))) = 0

To solve the equation log5(log3(log2(x^2+7x))) = 0, we need to apply logarithmic properties and algebraic techniques. Let's break down the steps to solve this equation.

Step 1: Simplify the equation using logarithmic properties. We can start by applying the logarithmic properties to simplify the equation. The equation can be rewritten as follows:

log5(log3(log2(x^2+7x))) = 0

Step 2: Apply the inverse property of logarithms. Since the logarithm of a number to its base is equal to 1, we can apply the inverse property of logarithms to eliminate the logarithms in the equation. This gives us:

log3(log2(x^2+7x)) = 5^0

Simplifying further:

log3(log2(x^2+7x)) = 1

Step 3: Apply the inverse property of logarithms again. Using the inverse property of logarithms once more, we can eliminate the logarithm of base 3:

log2(x^2+7x) = 3^1

Simplifying further:

log2(x^2+7x) = 3

Step 4: Convert the logarithmic equation into an exponential equation. To solve for x, we can convert the logarithmic equation into an exponential equation. In this case, the base of the logarithm is 2. Rewriting the equation in exponential form, we get:

2^3 = x^2+7x

Simplifying further:

8 = x^2+7x

Step 5: Rearrange the equation and solve for x. To solve the quadratic equation, we can rearrange it into standard form:

x^2 + 7x - 8 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:

(x + 8)(x - 1) = 0

Setting each factor equal to zero, we get:

x + 8 = 0 or x - 1 = 0

Solving for x in each equation:

x = -8 or x = 1

Therefore, the solutions to the equation log5(log3(log2(x^2+7x))) = 0 are x = -8 and x = 1.

Please note that the search results provided by You.com did not directly address the equation log5(log3(log2(x^2+7x))) = 0. However, the steps outlined above follow standard mathematical procedures for solving logarithmic equations.