Question

Find the value of the following with the help of log table : ³√102.5 × (0.0025)⁴.​

Answer 1

Answer:

Step-by-step explanation:

Let x=5872×0.058

Taking log both sides, we have

logx=log(5872×0.058)

logx=log5872+log0.058(∵logab=loga+logb)

logx=log(58.72×10 2 )+log(58×0 −3 )

logx=log58.72+2+log58−3(∵log10=1)

⇒1+logx=log58.72+log58

Using log table, we get

log58.72=1.77

og58=1.76

1+logx=1.77+1.76

⇒logx=3.53−1

⇒logx=2.53

⇒x=Antilog(2.53)=338.84

Therefore,

5872×0.058≈338.84

Answer 2

Answer:

The value is -9.77

Step-by-step explanation:

• As we know log(a.b) = log(a) + log(b),

       log (³√102.5 × (0.0025)⁴) = log(³√102.5) + log(0.0025)⁴

• Simplification of log(³√102.5):

      log(³√102.5) = $\log(102.5)^\frac{1}{3}$ = $\frac{1}{3} log(102.5)$ [as $\log a^x = x \log a$]

                                                 = $\frac{1}{3}log(\frac{1025}{10} )$ = $\frac{1}{3}(log1025 - log10)$ = $\frac{1}{3} (3.01 - 1)$

                                                                                                    = 0.67

• Simplification of log(0.0025)⁴:

        log(0.0025)⁴ = 4 log(0.0025) [as $\log a^x = x \log a$]

                              = $4\log\frac{25}{10000}$ = $4(\log 25 - \log 10^4)$ = $4 (\log25 -4 \log10)$

                                                                                 = 4 (1.39 - 4) = - 10.44

• Solution:  log(³√102.5) + log(0.0025)⁴ = 0.67 - 10.44 = -9.77

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