Question

if log2=x(base 10),log3=y(base 10) then find log1.2 in terms of x and y​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

We are aware of the Logarithmic formula that :

1.

$log_{a}(xy) = log_{a}(x) + log_{a}(y)$

2.

$log_{a}(a) = 1$

3.

$\displaystyle \: log_{a} \bigg( \frac{x}{y} \bigg) = log_{a}(x) - log_{a}(y)$

GIVEN

$log_{10}(2) = x \: \: and \: \: log_{10}(3) = y$

TO DETERMINE

$log_{10}(1.2)$

EVALUATION

$\displaystyle \: log_{10}(1.2)$

$= \displaystyle \: log_{10} \bigg( \frac{12}{10} \bigg)$

$= \displaystyle \: log_{10}(12) - log_{10}(10)$

$= \displaystyle \: log_{10}(2 \times 2 \times 3) - 1$

$= \displaystyle \: log_{10}(2) + log_{10}(2) + log_{10}(3) - 1$

$= x + x + y - 1$

$= 2x + y - 1$