Evaluate using maths table or calc 2log5-1/2 log16+2log40
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.
To evaluate the expression 2log5 - (1/2)log16 + 2log40, we need to apply properties of logarithms and simplify the expression step-by-step.
Step 1: Start with the given expression:
2log5 - (1/2)log16 + 2log40
Step 2: Apply the property of logarithms where the exponent in the logarithm can be brought down as a coefficient:
log5^2 - log16^(1/2) + log40^2
Step 3: Simplify the logarithmic terms using the rules of exponents:
log25 - (1/2)log4 + log1600
Step 4: Apply the property of logarithms where the sum of two logarithms can be written as the logarithm of their product:
log25 - log4^(1/2) + log1600
Step 5: Simplify the logarithmic terms using the rules of exponents:
log25 - log(2^2) + log1600
Step 6: Simplify further:
log25 - log4 + log1600
Step 7: Use the properties of logarithms again to simplify:
log(25/4) + log1600
Step 8: Use the properties of logarithms to combine the two logarithms into one:
log(25/4 * 1600)
Step 9: Calculate the value inside the logarithm:
log(40000)
Step 10: Finally, evaluate the logarithm:
log(40000) ≈ 4.602
So, the simplified expression 2log5 - (1/2)log16 + 2log40 evaluates to approximately 4.602.