Step 1: Identify the given value and the expression to evaluate.
Given: log6.5=0.8129
Evaluate: 2log6.5+log650
Step 2: Substitute the given value of log6.5 into the expression.
2log6.5+log650=2(0.8129)+log650
Step 3: Simplify log650 using the properties of logarithms.
We can write 650 as 6.5×100.
Using the logarithm property log(AB)=logA+logB:
log650=log(6.5×100)
log650=log6.5+log100
Since the base of the logarithm is not specified, we assume it is base 10.
Therefore, log100=2 (because 102=100).
Substitute the value of log6.5:
log650=0.8129+2
log650=2.8129
Step 4: Substitute the value of log650 back into the expression and calculate.
2(0.8129)+2.8129
1.6258+2.8129
4.4387
The final answer is 4.4387.