Solve the equation.
log 6.44 + 3 log x - log x^2 = log 6.44 + 3
The same ambiguous question was posted here
and I answered it as I understood it.
You did not respond at the time
http://www.jiskha.com/display.cgi?id=1271367239
I just noticed you changed it slightly
Now it becomes
3 log x - log x^2 = 3
log x^3 - log x^2 = 3
log (x^4/x^2) = 3
log x = 3
x = 10^3 = 1000
Thank you so much. I understand it now.
To solve the given equation:
1. Start by simplifying the equation using logarithmic properties. Specifically:
- log a + log b = log (a * b)
- log a - log b = log (a / b)
- log a^b = b * log a
Applying these properties, the equation becomes:
log 6.44 + log x^3 - log x^2 = log 6.44 + 3
2. Use the property log a + log b = log (a * b) to combine the first two logarithms:
log (6.44 * x^3) - log x^2 = log 6.44 + 3
3. Use the property log a - log b = log (a / b) to simplify further:
log [(6.44 * x^3) / x^2] = log 6.44 + 3
4. Simplify the equation:
log (6.44 * x) = log 6.44 + 3
5. Now that the logarithms are equal, we can drop the logarithm notation and solve the equation algebraically:
6.44 * x = 6.44 + 3
6. Simplify further:
6.44 * x = 9.44
7. Divide both sides of the equation by 6.44 to solve for x:
x = 9.44 / 6.44
Calculating this division gives us:
x ≈ 1.465
Therefore, the solution to the given equation is x ≈ 1.465.