Question

A) 2 logả x + 5loga x - 3 = 0;​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation 2logₐx + 5logₐx - 3 = 0, we can combine the logarithms using the properties of logarithms and then solve for x. Here's the step-by-step solution:

Step 1: Combine the logarithms using the product rule of logarithms: 2logₐx + 5logₐx - 3 = logₐ(x²) + logₐ(x⁵) - 3

Step 2: Apply the sum rule of logarithms: logₐ(x²) + logₐ(x⁵) - 3 = logₐ(x² * x⁵) - 3

Step 3: Simplify the expression inside the logarithm: logₐ(x² * x⁵) - 3 = logₐ(x⁷) - 3

Step 4: Set the expression inside the logarithm equal to 1: logₐ(x⁷) - 3 = 1

Step 5: Add 3 to both sides of the equation: logₐ(x⁷) = 4

Step 6: Rewrite the equation in exponential form: a⁴ = x⁷

Step 7: Take the seventh root of both sides to isolate x: x = (a⁴)^(1/7)

Therefore, the solution to the equation 2logₐx + 5logₐx - 3 = 0 is x = (a⁴)^(1/7).