Question

• Evaluate each of the following in terms of x and y, if it is given that x = log2(3) and y=log2(5) (i) log2(6750)​

Answer 1

$\begin{gathered} \\ \bigstar \: \underline \pink{ \frak{ \large{Given :-}} } \\ \end{gathered}$

$\begin{gathered} \qquad \: \: \: \: \: \: \: \: \: \: \bullet \: \: \: \sf \: x = log_{2}3 \\ \end{gathered}$

$\begin{gathered} \qquad \: \: \: \: \: \: \: \: \: \: \bullet \: \: \: \sf \: y = log_{2}5\\ \end{gathered}$

$\begin{gathered} \qquad \: \: \: \: \: \: \: \: \: \: \bullet \: \: \: \sf \: log_{2}60\\ \end{gathered}$

$\begin{gathered} \\ \bigstar \: \underline \pink{ \frak{ \large{Solution :-}} } \\ \end{gathered}$

$\begin{gathered} \\ \: \: \: \sf \: log_{2}60\\ \end{gathered}$

$\begin{gathered} \\ \qquad \: \: \: \: \mapsto \: \: \: \sf \: log_{2}(20 \times 3)\\ \end{gathered}$

$\begin{gathered} \\ \qquad \: \: \: \: \mapsto \: \: \: \sf \: log_{2}20 + log_{2} 3\\ \end{gathered}$

$\begin{gathered} \\ \qquad \: \: \: \: \mapsto \: \: \: \sf \: log_{2}(4 \times 5) + log_{2} 3\\ \end{gathered}$

$\begin{gathered} \\ \qquad \: \: \: \: \mapsto \: \: \: \sf \: log_{2}4 + log_{2}5+ log_{2} 3\\ \end{gathered}$

$\begin{gathered} \\ \qquad \: \: \: \: \mapsto \: \: \: \sf \: 2log_{2}2 + log_{2}5+ log_{2} 3\\ \end{gathered}$

$\begin{gathered} \\ \qquad \: \: \: \: \mapsto \: \: \: \sf \: 2 + log_{2}5+ log_{2} 3\\ \end{gathered}$

$\begin{gathered} \\ \qquad \: \: \: \: \mapsto \: \: \: \sf \: \boxed{ \rm 2 + y+ x}\\ \end{gathered}$