Verified Answer :

f(x) = ㏒(10x)
f(x) = ㏒₁₀(10x)

10y = 6
 10    10
    y = 0.6

f(x) = ㏒₁₀(10x)
0.6 = ㏒₁₀(10x)
\(10^{0.6} = 10x\)
\(10^{\frac{3}{5}} = 10x\)
\(\sqrt[5]{10^{3}} = 10x\)
\(\sqrt[5]{1000} = 10x\)
\(\frac{\sqrt[5]{1000}}{10} = x\)
\(\frac{3.98}{10} \approx x\)
\(0.398 \approx x\)

The given function is

f(x)= log 10 x

Taking base as 10

\(y=\log_{10}10 +\log_{10}x\)→→Using the property of, log a b= log a + log b

→y = 1 + \(\log_{10}x\) as, \(\log_{10}10=1\)

we have to approximate the value of y in the equation

→10 y = 6

→y=\(\frac{6}{10}\)

\(\frac{6}{10}\)= 1 + \(\log_{10}x\)  

\(\log_{10}x\) =  \(\frac{-4}{10}\)

x= \((10)^{\frac{-4}{10}}\)=\((10)^{-0.4}\)=0.398

Solving graphically,

we get , x= 0.398 for , y= \(\frac{6}{10}\)=.6

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