log3(4x+1)-log3(3x-5)=2
log3(4x+1)-log3(3x-5)=2
log3( (4x+1)/(3x-5)) = 2
(4x+1)/(3x-5) = 3^2 = 9
27x - 45 = 4x + 1
carry on
Abigail
If log10y+3log10*=2, Express y in term of x.
Solve the equation log3,4x+1-log3,3x-5=2
Using the logarithmic identity,
log base a (M/N) = log base a M - log base a N,
we can rewrite the given equation as:
log3 (4x+1) - log3 (3x-5) = 2
log3 [(4x+1)/(3x-5)] = 2
3^2 = 9, so we can rewrite the equation as:
(4x+1)/(3x-5) = 9
Multiplying both sides by 3x-5, we get:
4x + 1 = 9(3x-5)
Simplifying and solving for x, we get:
4x + 1 = 27x - 45
24x = 46
x = 46/24
Simplifying, we get:
x = 23/12
Therefore, the solution to the equation is:
x = 23/12.
Let's solve this equation step-by-step, but before that, let me try to lighten the mood a bit. Why did the mathematician go to war? Because he heard people were carrying weapons of math instruction!
Now, back to the equation. To begin with, we can simplify it using logarithmic properties. According to the quotient rule, we can subtract the logarithmic terms:
log3[(4x+1)/(3x-5)]=2
Now, we can rewrite this equation as an exponential equation:
3^2 = (4x + 1)/(3x - 5)
Simplifying further,
9 = (4x + 1)/(3x - 5)
To eliminate the fraction, we can cross-multiply:
9(3x - 5) = 4x + 1
Expanding the equation:
27x - 45 = 4x + 1
Combining like terms:
27x - 4x = 1 + 45
23x = 46
Dividing both sides by 23:
x = 2
So, the solution to the equation log3(4x + 1) - log3(3x - 5) = 2 is x = 2.
I hope that brought a smile to your face! If you have any more questions, feel free to ask!
To solve the equation log3(4x+1) - log3(3x-5) = 2, we can use the properties of logarithms to simplify the expression and isolate the variable.
The first property we can use is the quotient rule, which states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. In this case, we can rewrite the equation as a single logarithm:
log3[(4x+1)/(3x-5)] = 2
Next, we can use the fact that if the logarithm of a number is equal to another number, then the exponent of the base raised to that logarithm is equal to the original number. In this case, we have:
3^2 = (4x+1)/(3x-5)
Simplifying the equation further:
9 = (4x+1)/(3x-5)
To eliminate the fraction, we can cross-multiply:
9(3x-5) = 4x+1
Expanding and simplifying the equation:
27x - 45 = 4x + 1
Combine the like terms:
27x - 4x = 1 + 45
23x = 46
Finally, we can solve for x by dividing both sides of the equation by 23:
x = 46/23
Therefore, the solution to the equation log3(4x+1) - log3(3x-5) = 2 is x = 2.