we haven't discussed log properly yet! It's supossed to be on the RAT, but IDK. . .
this is about as much as I know:
if you have log(X) 2401 = 4, then x equals 7.
One of the simulated questions asks to express 3log(2) p + 4log(2) Q - 2log(2) R. please help.
That would be log(base 2) of
p^3 Q^4/R^2
The log of any number x to a power n is n log x, with the logs taken to the same base.
c.f. rules of logarithms on wikipedia.
Sure! I can help explain how to solve the expression 3log(2) p + 4log(2) Q - 2log(2) R.
To begin, it's important to understand the logarithmic properties. In this case, we are dealing with the logarithm base 2, which is denoted by log(2). The logarithm of a number is the exponent to which the base must be raised to obtain that number.
Now, let's break down the expression step by step:
1. 3log(2) p:
Here, we have the logarithm base 2 of p raised to the power of 3. To simplify this, we can use the property of logarithms that states log(a) b^n = nlog(a) b. Applying this property, we get:
3log(2) p = log(2) p^3
2. 4log(2) Q:
Similarly, we have the logarithm base 2 of Q raised to the power of 4. Using the same property from above, we can simplify this as follows:
4log(2) Q = log(2) Q^4
3. -2log(2) R:
Here, we have the logarithm base 2 of R raised to the power of -2. To simplify this, we can rewrite it as the reciprocal of R raised to the power of 2:
-2log(2) R = log(2) (1/R^2)
Now, we can substitute the above simplified expressions back into the original expression:
3log(2) p + 4log(2) Q - 2log(2) R = log(2) p^3 + log(2) Q^4 + log(2) (1/R^2)
To simplify further, we can use another property of logarithms that states log(a) b + log(a) c = log(a) (b * c). Applying this property to the above expression, we get:
log(2) p^3 + log(2) Q^4 + log(2) (1/R^2) = log(2) [(p^3 * Q^4) * (1/R^2)]
Therefore, the final expression is:
3log(2) p + 4log(2) Q - 2log(2) R = log(2) [(p^3 * Q^4) * (1/R^2)]
Remember to simplify the numerical part and perform any additional mathematical operations as needed.