Which equation is equivalent to 3 ln 2 – ln 4 + 5 ln x = ln 3 + 2 ln 5?

ln 2x5 = ln 75
ln (5x + 2) = ln 75
ln 2x5 = ln 13
ln (5x + 4) = ln 96

the people above messed up; its supposed to be an exponent.

the way you do this problem is

- so 3ln2 is 2^3 and ln4 can be written as 2^2 making it ln 2^5.
- then for the other side its 5^2 which is 25 then x 3 which is 75.

the actual answer is ln2x^5 = ln75.

welcome :)

You gave me faulse information and i do not appreciate it because i trusted you 😔

3 ln 2 – ln 4 + 5 ln x = ln 3 + 2 ln 5

ln 2^3 - ln4 + ln x^5 = ln 3 + ln 5^2
ln ((8x^5)/4) = ln (75)

none of those match this

left in log form, I had
ln (8x^5/4) = ln 75

none of your choices match this.

To find the equation that is equivalent to the given expression, we need to simplify the terms using logarithm properties and then solve for x.

Step 1: Apply the logarithm properties
Recall the properties of logarithms:
1. ln(a) + ln(b) = ln(a*b)
2. ln(a) - ln(b) = ln(a/b)
3. ln(a^k) = k * ln(a)

Using these properties, let's simplify the given expression:
3 ln 2 - ln 4 + 5 ln x = ln 3 + 2 ln 5

First, apply property 3 to the terms that have exponents:
ln(2^3) - ln 4 + ln(x^5) = ln 3 + ln(5^2)

Simplifying further:
ln(8) - ln 4 + ln(x^5) = ln 3 + ln(25)

Now, apply properties 1 and 2:
ln(8/4) + ln(x^5) = ln(3*25)

Simplifying inside the logarithms:
ln(2) + ln(x^5) = ln(75)

Next, apply property 3 to the remaining term:
ln(2) + 5 ln(x) = ln(75)

Step 2: Combine the logarithms
Combine the terms on the left-hand side into a single logarithm using property 1:
ln(2x^5) = ln(75)

Step 3: Remove the logarithms
To remove the logarithms, we need to take the exponential of both sides of the equation. Since ln(x) represents the natural logarithm (base e), we will use base e exponential, which is the natural exponential (e^x).

Applying the exponential function, we get:
e^(ln(2x^5)) = e^(ln(75))

Simplifying further:
2x^5 = 75

Step 4: Solve for x
Divide both sides of the equation by 2 to isolate x^5:
x^5 = 75/2

Finally, take the fifth root of both sides to solve for x:
x = (75/2)^(1/5)

Therefore, the equation equivalent to 3 ln 2 – ln 4 + 5 ln x = ln 3 + 2 ln 5 is x = (75/2)^(1/5).