Question

2^log8(5x-3)=4 решить уравнение

Answer 1

Решение смотри на фотографии

Answer 2

To solve the equation 2^(log8(5x-3)) = 4, we can rewrite it using the property of logarithms that states log(base a)(a^b) = b:

log8(5x-3) = log2(4)

Since the bases are different, we can convert the equation to a common base. In this case, let's convert both sides to base 2:

(log2(5x-3))/(log2(8)) = log2(4)

Simplifying the equation further:

(log2(5x-3))/3 = 2

Multiplying both sides of the equation by 3:

log2(5x-3) = 6

Now, we can rewrite the equation as an exponential equation:

2^(log2(5x-3)) = 2^6

Simplifying the equation further:

5x-3 = 64

Adding 3 to both sides:

5x = 67

Finally, divide both sides by 5 to solve for x:

x = 67/5

Therefore, the solution to the equation is x = 67/5.