log72-log(2x/3)=0
I hope you are familiar with the standard rules of logs, then...
log72-log(2x/3)=0
log10 (72 ÷ 2x/3) = 0
72(3/(2x) = 10^0
216/(2x) = 1
2x = 216
x = 108
To solve the equation log72 - log(2x/3) = 0, we can use the properties of logarithms.
Step 1: Combine the logarithms using the quotient rule of logarithms:
log72 - log(2x/3) = log(72 / (2x/3))
Step 2: Simplify the expression inside the logarithm:
log(72 / (2x/3)) = log(72 * (3/2x))
Step 3: Simplify further, cancelling out any common factors:
log(72 * (3/2x)) = log(36/2x)
Step 4: Apply the power rule of logarithms to eliminate the logarithm:
36/2x = 10^0
Step 5: Simplify 10^0, which is equal to 1:
36/2x = 1
Step 6: Cross-multiply to solve for x:
36 = 2x
Step 7: Divide both sides of the equation by 2:
x = 18
Therefore, the solution to the equation log72 - log(2x/3) = 0 is x = 18.
To solve the equation log(72) - log(2x/3) = 0, we can use the laws of logarithms. The equation combines two logarithms with the subtraction operation, so we can simplify it using the quotient rule of logarithms, which states that log(a) - log(b) = log(a/b).
Applying this rule to our equation, we have:
log(72) - log(2x/3) = 0
log(72/(2x/3)) = 0
To remove the logarithm and solve for x, we need to exponentiate both sides of the equation. Exponentiating means raising both sides to the power of 10 since the base of the logarithm is 10. This will cancel out the logarithm on the left side.
10^(log(72/(2x/3))) = 10^0
The logarithm and exponentiation functions are inverse operations, so they cancel each other out, resulting in:
72/(2x/3) = 1
Next, we can simplify the equation by multiplying both sides by (2x/3):
(2x/3) * (72/(2x/3)) = (2x/3) * 1
72 = 2x
Finally, we solve for x by dividing both sides of the equation by 2:
72/2 = x
36 = x
So, the solution to the equation log(72) - log(2x/3) = 0 is x = 36.