Question

If "f(log₅x) - log₅(x + 3) = 2", then "log₅__________ = 2".

a) x + 3
b) x - 3
c) x
d) 1/x

Answer 1

To find the value of x that satisfies the equation f(log5x) - log5(x + 3) = 2, we can simplify the equation, combine the logarithms, convert to exponential form, and solve for x. The value of x that satisfies the equation is -75/24.

Step-by-step explanation:

To find the value of x that satisfies the equation f(log5x) - log5(x + 3) = 2, we need to solve for x. First, we can simplify the equation by applying the property that the logarithm of the quotient of two numbers is the difference of the logarithms of the numbers. Therefore, we have:

f(log5x) - log5(x + 3) = 2
log5x - log5(x + 3) = 2

Next, we can combine the logarithms using the property that the logarithm of the product of two numbers is the sum of the logarithms of the numbers. This gives us:

log5(x/(x + 3)) = 2

Finally, we can convert this equation into exponential form to isolate x. Therefore, we have:

52 = x/(x + 3)

Simplifying, we get:

25 = x/(x + 3)

Multiplying both sides by (x + 3), we get:

25(x + 3) = x

Expanding, we get:

25x + 75 = x

Moving the x term to the left side and the constant term to the right side, we get:

24x = -75

Dividing both sides by 24, we find:

x = -75/24

Hence, the value of x that satisfies the equation is -75/24.