Simple query. plz tell me in brief. How will u slove this
-3 log 3 + log 2 + 2 log 4
Plz explain
what are you solving for? What is the question?
im solving for this log problem. The question is wht i ve asked
To solve the expression -3log3 + log2 + 2log4, we can use the following logarithmic properties:
1. Product rule: log(a) + log(b) = log(ab).
2. Power rule: log(a^b) = blog(a).
3. Negative rule: log(a) - log(b) = log(a/b).
Let's apply these rules to the given expression step by step:
Step 1: Simplify -3log3.
Since -3 is a constant multiplier, we can use the power rule to rewrite -3log3 as log(3^(-3)):
-3log3 = log(3^(-3)).
Step 2: Simplify 2log4.
Similarly, using the power rule, we rewrite 2log4 as log(4^2):
2log4 = log(4^2).
Now, let's rewrite the expression using these simplifications:
-3log3 + log2 + 2log4
= log(3^(-3)) + log2 + log(4^2)
= log(3^(-3)) + log2 + log(16)
Step 3: Combine the logarithms.
Using the product rule, we can combine the logarithms with the same base:
= log[3^(-3) * 2 * 16]
= log[1/27 * 32]
= log(32/27)
So, the simplified expression is log(32/27).