Question

3. Given log 100 = 2, log 101 = 2.0043,log 103 = 2.0128, log 104 = 2.0170, find log 102.​

Answer 1

Step-by-step explanation:

given,

log101=2.0043

log103=2.0128

therefore log102=log100+log103-log101

log102=2+2.0128-2.0043

log102=2+0.0085

log102= 2.0085

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Answer 2

Answer:

So the value of lo(102) is 2.0085.

Step-by-step explanation:

• The given data:  log 100 = 2,         log 101 = 2.0043,

                                log 103 = 2.0128,    log 104 = 2.0170,

• We can write 102 like, 102 = $\frac{101 \times 104}{103}$

   Now taking log on both sides,  log(102) = log($\frac{101 \times 104}{103}$)

• Evaluating the value of log($\frac{101 \times 104}{103}$):

log($\frac{101 \times 104}{103}$) = log(101 × 104) - log(103) [as we know log(a/b) = loga - logb]

                   = log(101) + log(104) - log(103)    [ as log(a.b) = log a + log b]

                   = 2.0043 + 2.0170 - 2.0128    [by putting all the values]

                   = 4.0213 - 2.0128

                   = 2.0085

    So the value of lo(102) is 2.0085.

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