this reads the log of 4 times x squared, divided by (3 times y times z) the log statement applies to everything to the right.
Rewrite the original equation as:
Log(4x^2) - log(3yz)
Rewrite log(4x^2) as log(4) + log(x^2)
Rewrite log(4) as 2log(2)
Rewrite log(x^2) as 2log(x)
Separate log(3yz) into 3 logs: log(3), log(y) and log(z)
Now combine them to get:
2log(2) + 2log(x) - log(3) - log(y) - log(z)
The decomposition of the logarithmic expression Log((4)/(3yz)) leads to the end result: Log(4) + Log() - Log(3) - Log(y) - Log(z). The given expression is separated into individual logarithms applying the logarithmic rules.
The decomposition of the logarithmic expression Log((4x2)/(3yz)) according to the laws of logarithms can be done as follows:
Using the rule that log(a/b) = log(a) - log(b), we can first split the expression into two parts: Log(4x2) - Log(3yz).
From there, we can apply the rule that log(ab) = log(a) + log(b) to split these further. So, Log(4x2) becomes Log(4) + Log(x2), and Log(3yz) becomes Log(3) + Log(y) + Log(z).
Finally, we substitute these back into the original expression to get the final decomposition: Log(4) + Log(x2) - Log(3) - Log(y) - Log(z).
#SPJ12
Answer: Yes, the given sequence is geometric with common ration 2.
Step-by-step explanation: The given sequence is:
6, 12, 24, 48, . . ..
We are to check whether the above sequence is geometric or not. If it is geometric, we are to find the common ratio.
Geometric sequence - a sequence of numbers where each term is found by multiplying by a constant to the preceding term. This constant is called the common ratio, r.
The consecutive terms of the given sequence can be written as:
We can see that
Therefore, each term is formed by multiplying 2 to the preceding term.
Thus, the given sequence is a geometric sequence with common ratio 2.