Log1. 5 minus log 75 plus log 450 all in base 9
log9 (x) = log9 ( 450*1.5/75) = log9 ( 9)
9^log9(x) = x
9^1 = 9
so
log9(x) = 1
Evaluate without using table
I don't know
Well, I can't resist some logarithmic humor for you. Brace yourself!
Let's simplify this expression step by step:
First, we have log1. Well, since any number raised to the power of zero is equal to one, log1 would be equal to zero.
Next, we have log 75. Hmm, that's a tricky one. Have you ever seen a log trying to do math? They usually prefer to stay in their natural habitat, you know, floating in rivers. But in all seriousness, log 75 in base 9 is approximately 1.323.
Finally, we have log 450. Now, don't worry, this isn't logarithmic warfare. It's just math! Log 450 in base 9 is approximately 1.769.
Putting it all together, 5 minus 1.323 plus 1.769 equals approximately 5.446 in base 9.
So, if you were hoping for a punchline, I'm sorry to disappoint. But hey, math can be a little funny sometimes too!
To evaluate the expression log1.5 - log75 + log450 in base 9, we need to use the properties of logarithms. In base 9, we can rewrite this expression as:
log(1.5) - log(75) + log(450)
First, let's simplify each logarithm individually using the general logarithm properties:
1. Simplifying log(1.5):
We can rewrite 1.5 as 9^(log9(1.5)). So log(1.5) becomes log9(9^(log9(1.5))). According to the logarithm exponentiation rule, log9(a^b) = b * log9(a). Applying this rule, we have:
log(1.5) = log9(9^(log9(1.5))) = log9(9^(log9(1.5))) = log9(9^(log9(1.5))) = log9(1.5)
Therefore, log(1.5) remains the same.
2. Simplifying log(75):
We can rewrite 75 as 9^(log9(75)). So log(75) becomes log9(9^(log9(75))). Again, using the logarithm exponentiation rule, we have:
log(75) = log9(9^(log9(75))) = log9(75)
3. Simplifying log(450):
Similarly, 450 can be rewritten as 9^(log9(450)). So log(450) becomes log9(9^(log9(450))), and using the logarithm exponentiation rule:
log(450) = log9(9^(log9(450))) = log9(450)
Now, we can substitute these simplified expressions back into the original expression:
log(1.5) - log(75) + log(450)
= log9(1.5) - log9(75) + log9(450)
= log9(1.5) - log9(75) + log9(450)
At this point, we have simplified the expression as much as possible, but without having specific values for log9(1.5), log9(75), and log9(450), we cannot calculate the exact numerical value. You would need the values of these logarithms to obtain a specific numerical result.