Question

$2\log_{10}5+\log_{10}36-\log_{10}9=$ কত?

Answer 1

$2\log_{10}5 + \log_{10}36 - \log_{10}9$

$=\log_{10}5^2+\log_{10}6^2-\log_{10}3^2$

$=\log_{10}(5^2 \times 6^2 \div 3^2)$

$=\log_{10}(25 \times 36 \div 9)$

$=\log_{10} \left(25 \times 36 \times \frac{1}{9}\right)$

$=\log_{10} \left(25\times\overset4{\bcancel{36}}\times\frac1{\bcancel9}\right)$

$=\log_{10}100$

$=\log_{10}10^2$

$=2\log_{10}10$

$=2 \times 1$

$=2$

Comments

Rules applied :

• $a \log_kM =\log_kM^a$
• $\log_kM+\log_kN =\log_k(MN)$
• $\log_kM–\log_kN =\log_k(M \div N) =\log_k \left(\frac{M}{N}\right)$
• $\log_kM^a =a \log_kM$
• $\log_aa =1$