Question

If log4=0.6020 find the value of 80

Answer 1

Answer:  The answer is 1.9030.

Step-by-step explanation:  We are given that log 4 = 0.6020 and we are to find the value of log 80.

We calculate this as follows:

$\log 80=\log(2\times4 \times 10)=\log 2+\log 4+\log 10\\\\\Rightarrow \log 80=\dfrac{1}{2}\log 4+\log 4+1\\\\\\\Rightarrow \log 80=\dfrac{1}{2}\times 0.6020+0.6020+1\\\\\\\Rightarrow \log 80=0.3010+0.6020+1\\\\\Rightarrow \log 80=1.9030.$

Thus, the required value is 1.9030.

Answer 2

"Answer: The logarithmic value of 80 is 1.9030

Given that log4 = 0.6020

We can factorise 80 into 2 times $4 \times 10$.

Such that the logarithmic value of 80can be written as,

log80 = log ($2 \times 4 \times 10$) = log2 + log4 + log10

          = $\frac {1} {2} log4 + log4 + 1$                                                

          = $\frac {1} {2} (0.6020) + 0.6020 + 1$

          = 0.3010 + 0.6020 + 1

         = 1.9030 "