Using the graph of f(x) = log10x below, approximate the value of y in the equation 10y = 6
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