Question

Find the value of the expression \(\rm \frac{log_{4}3 \times log_{a} 4 \times log_{3}a}{log_{6}3}-{{log_{3}{2}}}\)
5. log₃ 2

Answer 1

Correct Answer - Option 4 : 1

Concept:

• \(\rm log_bm.log_ab = log_am\)
• \(\rm log_ba =\frac{1}{ log_ab}\)

Calculation:

Here we have to find the value of \(\rm \frac{log_{4}3 \times log_{a} 4 \times log_{3}a}{log_{6}3}-{{log_{3}{2}}}\)

⇒ \(\rm \frac{log_{4}3 \times log_{a} 4 \times log_{3}a}{log_{6}3}-{{log_{3}{2}}} = \rm \frac{log_{4}3 \times log_{3}4}{log_{6}3}-{{log_{3}{2}}}\)         ( ∴ \(\rm log_bm \times log_ab = log_am\))

=  \(\rm \frac{log_{3}3}{log_{6}3}-{{log_{3}{2}}}\)           ( ∴ \(\rm log_bm.log_ab = log_am\))

= \(\rm \frac{1}{log_{6}3}-{{log_{3}{2}}}\)

= \(\rm {log_{3}6}-{{log_{{3}}2}}\)           ( ∴ \(\rm log_ba =\frac{1}{ log_ab}\))

=  \(\rm {log_{3}(\frac{6}{2})}\)

= \(\rm {log_{3}3} = 1\)

Hence, option 4 is correct.