Find the value of x given that
Log(15-5x)-1 log(3x-2)
Log(15-5x) - 1 = Log(3x-2).
Log(15-5x) - Log(3x-2) = 1,
Recall that Log A - Log B = Log(A/B)
Log((15-5x)/(3x-2)) = 1, Log10 = 1
Therefore, (15-5x)/(3x-2) = 10,
15-5x = 30x-20,
X =
Seems incomplete. Should there be an equals sign somewhere?
Also, if you could post your work for your questions, that would help us help you.
assuming that you meant
log(15-5x)-1 = log(3x-2)
then recall that log10 = 1, so that's the same as
log ((15-5x)/10) = log (3x-2)
if the logs are the same, so are the numbers:
(15-5x)/10 = 3x-2
and you can finish it up.
X=1
To find the value of x in the equation Log(15-5x)-1 = log(3x-2), we need to solve for x.
First, let's simplify the equation by using logarithmic properties. The property we will use is log(a) - log(b) = log(a/b). Applying this property, we can rewrite the equation as:
log((15-5x)/(3x-2)) = 1
Now, exponentiate both sides of the equation with the base of the logarithm, which is 10. Exponentiating both sides will cancel out the logarithm:
10^(log((15-5x)/(3x-2))) = 10^1
Simplifying further:
(15-5x)/(3x-2) = 10
Next, we can cross-multiply to eliminate the fraction:
15 - 5x = 10(3x-2)
Simplify the right side:
15 - 5x = 30x - 20
Rearrange the equation by bringing similar terms together:
30x + 5x = 15 + 20
Combine like terms:
35x = 35
Divide both sides by 35:
x = 1
Therefore, the value of x in the given equation is 1.