Evaluate using maths table or calc 2log5-1/2 log16+2log40

Answer 1

To evaluate the expression 2log5 - 1/2log16 + 2log40, we can use the logarithmic properties and rules to simplify it.

First, let's apply the power rule of logarithms:

2log5 = log5^2 = log25

Next, we can rewrite 1/2log16 as log16^(1/2) using the power rule:

log16^(1/2) = log√16 = log4

Lastly, we can use the product rule to simplify 2log40:

2log40 = log40^2 = log1600

So now our expression is log25 - log4 + log1600.

Using the quotient rule of logarithms, we can combine the terms:

log25 - log4 + log1600 = log(25/4) + log1600

Now, let's simplify the expression further.

Using the logarithmic identity loga + logb = log(ab), we can combine the logarithms:

log(25/4) + log1600 = log((25/4) * 1600)

Calculating the value inside the logarithm:

log((25/4) * 1600) = log(100 * 10) = log(1000) = 3

Therefore, 2log5 - 1/2log16 + 2log40 simplifies to 3.