Question

simplify 2 log 4 - 1/2 log 16 + 1​

Answer 1

Step-by-step explanation:

this is correct answer

Answer 2

The simplified value is 1.602

Given

2 log 4 - 1/2 log 16 + 1​

To Find

Simplify the expression 2 log2 log 4 - 1/2 log 16 + 1​

Solution

For any logarithmic expression:-

1. a logb = log(b^a)
2. 1/2loga = log(√a)
3. loga + logb = log(ab)
4. loga - logb = log(a/b)

hence,

2 log 4 - 1/2 log 16 + 1​      

= 2log4 - log√16 + 1                       [Using formula no. 2]

= log(4²) - log4 + 1                          [Using formula no.  1]

= log(4²/4) + 1                                 [Using formula no. 4]

= log4 + 1

= 0.602 + 1                                     [getting value of log4 from the calculator]

= 1.602

Therefore, the simplified value is 1.602

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