Question

Lg2x/ lg (4x - 15)= 2

Answer 1

это уравнение можно записать как

log4x-15 2x=2

2x=(4x-15)^2

2x=16x^2-120x+225

16x^2-122x+225=0

D=122^2-4*225*16=484

x1=122+22/32=4.5

x2=122-22/32=3.125

ответ х1=4.5

Answer 2

To solve the equation (lg2x / lg(4x - 15)) = 2, we can start by simplifying the expression.

Let's rewrite the equation in exponential form: 10^2 = lg(4x - 15) / lg2x

Now, we can eliminate the logarithms by converting them into exponential form: 100 = (4x - 15) / (2x)

Next, we can simplify the equation by multiplying both sides by 2x to eliminate the denominator: 100 * 2x = 4x - 15

Now, distribute the exponent to each term on the left side: (2^2)(x^2) = 4x - 15

Simplify the equation: 4x^2 = 4x - 15

Rearrange the equation to bring all terms to one side: 4x^2 - 4x + 15 = 0

Unfortunately, this is a quadratic equation, and it doesn't factor easily. To solve it, we can apply the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the coefficients are: a = 4 b = -4 c = 15

Substituting these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)^2 - 4 * 4 * 15)) / (2 * 4) = (4 ± √(16 - 240)) / 8 = (4 ± √(-224)) / 8

Since the expression inside the square root is negative, we have no real solutions to this equation.