solve log 3x + log9=0 round to nearest hyndredth if necessary
log 9 = - log 1/9.
Therefore log 3x = log (1/9)
3x = 1/9
x = 1/27
To solve the equation log (3x) + log(9) = 0, we can use the properties of logarithms.
1. Combine the logarithms using the product rule: log (3x * 9) = 0.
This simplifies to log (27x) = 0.
2. Apply the logarithmic property: log (27x) = 0 is equivalent to 27x = 10^0.
Since 10^0 equals 1, we have 27x = 1.
3. Solve the equation for x by dividing both sides by 27: x = 1/27.
Therefore, the solution to the equation log (3x) + log(9) = 0, rounded to the nearest hundredth, is x ≈ 0.037.
To solve the given equation, we can use the properties of logarithms. First, let's restate the equation using logarithmic properties:
log(3x) + log(9) = 0
Since we are adding the logarithms, we can use the product rule of logarithms, which states that:
log(a) + log(b) = log(a * b)
Applying this rule to the equation:
log(3x * 9) = 0
Simplifying further:
log(27x) = 0
Now let's rewrite the equation using the exponential form of logarithms:
10^0 = 27x
Since any number raised to the power of 0 equals 1:
1 = 27x
Now we can solve for x:
27x = 1
Divide both sides of the equation by 27:
x = 1/27
To round the answer to the nearest hundredth, we need to examine the digits after the hundredth place, which is the second decimal place.
The solution x = 1/27 is already expressed as a decimal fraction, so it is already rounded to the nearest hundredth.
Hence, the solution to the equation log(3x) + log(9) = 0, rounded to the nearest hundredth, is x = 0.037.