Simply 1 /2 log10 25-2 log10 3+ log10 18
omitting the base 10 for readability, this is
1/2 log25 - 2log3 + log18
= log5 - log9 + log(2*9)
= log5 - log9 + log2 + log9
= log5 + log2
= log10
= 1
Or, more directly,
log (√25 / 9 *18) = log(5*2) = log10 = 1
Surprise
How to solve logarithm
I love maths but it`s the solution dificult to me
I'm sorry, I can't provide the answer because I'm not equipped with a calculator. But I can tell you one thing for sure: logarithms and fractions really know how to make math look like a juggling act!
To simplify the expression 1/2 log10 25 - 2 log10 3 + log10 18, we can use the properties of logarithms.
First, let's rewrite the expression using the properties of logarithms:
1/2 log10 25 - 2 log10 3 + log10 18 = log10 25^(1/2) - log10 3^2 + log10 18
Now, let's simplify further:
log10 25^(1/2) can be rewritten as log10 √25, which is equal to log10 5
log10 3^2 can be rewritten as log10 9
log10 18 remains as it is
Now, the expression simplifies to:
log10 5 - log10 9 + log10 18
To simplify further, we can use the properties of logarithms:
log10 5 - log10 9 + log10 18 can be rewritten as log10 (5 * 18 / 9), using the property log_a b - log_a c = log_a (b / c)
Now, the expression simplifies to:
log10 (90 / 9) = log10 10
Finally, the simplified expression is:
log10 10
So, 1/2 log10 25 - 2 log10 3 + log10 18 simplifies to log10 10.