Question

5 log(2) x - 3 log(7) 49= 2 log(2) x

Answer 1

5 log(2) x - 3 log(7) 49= 2 log(2) x

5 log₂ x -  2 log₂ x = 3 log₇49    ОДЗ х>0

3 log₂x  = 3 log₇ 49

log₂ x  =  log₇7²

log₂ x  =  2 log₇7

log₂ x  =  2

х=2²= 4

Answer 2

To solve the given equation, let's simplify each term using the properties of logarithms.

Using the logarithmic identity log(base b) (a^c) = c * log(base b) a, we can simplify the equation as follows:

5 log(2) x - 3 log(7) 49 = 2 log(2) x

5 log(2) x - 3 log(7) 7^2 = 2 log(2) x

5 log(2) x - 3 log(7) 2^2 = 2 log(2) x

5 log(2) x - 3 log(7) 2^2 = 2 log(2) x

5 log(2) x - 3 * 2 log(7) 2 = 2 log(2) x

5 log(2) x - 6 log(7) 2 = 2 log(2) x

5 log(2) x - 6 * 2 log(7) = 2 log(2) x

5 log(2) x - 12 log(7) = 2 log(2) x

Now, we can combine the logarithms with the same base:

5 log(2) x - 12 log(7) = 2 log(2) x

To further simplify, let's isolate the logarithmic terms on one side of the equation:

5 log(2) x - 2 log(2) x = 12 log(7)

(5 - 2) log(2) x = 12 log(7)

3 log(2) x = 12 log(7)

Divide both sides of the equation by 3 log(2):

log(2) x = 4 log(7)

Now, using the logarithmic identity log(base b) (a^c) = c * log(base b) a, we can write:

log(2) x = log(7^4)

Since the logarithm function is one-to-one, we can equate the expressions inside the logarithms:

2^log(2) x = 7^4

x = 7^4

x = 2401

Therefore, the solution to the equation is x = 2401.