Question

Solve: [(log10 X – 3)/2] + [(11 – log10x)/3] = 2​

Answer 1

Answer:

The value of X is 0.1

Step-by-step explanation:

Given: $\tt{ \dfrac{\log_{10}X - 3}{2} \ +\ \dfrac{11 - \log_{10}X}{3} = 2 }$

$\tt{ \implies \dfrac{3(\log_{10}X - 3) + 2(11 - \log_{10}X)}{6} = 2 }$

$\tt{ \implies 3\log_{10}X - 9 + 22 - 2\log_{10}X = 6\times2 = 12 }$

$\tt{ \implies \log_{10}X + 13 = 12 }$

$\tt{ \implies \log_{10}X = 12-13 = -1 }$

$\tt{ \implies X = 10^{-1} }$

$\tt{ \implies X = 0.1 }$

Formulas :-

1) $\tt{ \log_{a}b = c \implies b = a^{c} }$

2) $\tt{ \log_{a}(mn) = \log_{a}m + \log_{a}n}$

3) $\tt{ \log_{a}(m/n) = \log_{a}m - \log_{a}n}$

4) $\tt{ \log_{a}(m^{n}) = n\,\log_{a}m}$

5) $\tt{ \log_{a}b = \dfrac{\log_{c}b}{\log_{c}a} }$