3log2+log20-log1.6
log ( 2^3 * 20/1.6)
log (8 * 20/1.6)
log 100
log 10^2
2 log 10
if these are base 10 logs then log10 = 1
so
2*1 = 2
Good
Thanks it really clear
To solve the expression 3log2 + log20 - log1.6, let's break it down step-by-step.
First, we can simplify the expression by applying logarithmic properties:
3log2 + log20 - log1.6
Since there are no exponents or bases other than 10 mentioned, we can infer that the logarithms are base 10 logarithms.
Next, we can use the properties of logarithms to simplify further:
1) The power rule: log(base b) (xy) = log(base b) x + log(base b) y
2) The quotient rule: log(base b) (x/y) = log(base b) x - log(base b) y
Using the power rule, we can rewrite the expression as:
log2^3 + log20 - log1.6
Simplifying further,
log(8) + log(20) - log(1.6)
Now, we can apply the quotient rule to obtain:
log(8 * 20 / 1.6)
Simplifying the expression inside the logarithm:
log(160)
Finally, evaluating the logarithm using a calculator or logarithm table, we find that log(160) ≈ 2.2041.
Therefore, the simplified expression 3log2 + log20 - log1.6 is approximately equal to 2.2041.