Question

Log _(8)2^5x-1=3 ПОЖАЛУЙСТА ПОМОГИТЕ РЕШИТЬ

Answer 1

Вроде так
Решение и ответ на фото

Answer 2

To solve the equation log _(8)2^(5x-1) = 3, we'll use logarithm properties to simplify and isolate the variable.

Step 1: Rewrite the equation using the logarithm base change rule. log _(8)2^(5x-1) = 3 can be rewritten as log(2^(5x-1)) / log(8) = 3.

Step 2: Simplify the logarithms. Using the property log_b(a^c) = c * log_b(a), we get: (5x - 1) * log(2) / log(8) = 3.

Step 3: Isolate the variable. Multiply both sides by log(8) to isolate (5x - 1): 5x - 1 = 3 * log(8) / log(2).

Step 4: Calculate the right-hand side. log(8) / log(2) is equal to log base 2 of 8, which is 3.

Step 5: Continue isolating the variable. Now, we have: 5x - 1 = 3 * 3 5x - 1 = 9

Step 6: Solve for x. Add 1 to both sides: 5x = 10

Finally, divide both sides by 5 to solve for x: x = 10 / 5 x = 2

So, the solution to the equation is x = 2.