Question

Evaluate the following without using tables : 
log₁₀8 + log₁₀25 + 2 log₁₀3 - log₁₀18

Answer 1

Consider the given expression
log₁₀8 + log₁₀25 + 2 log₁₀3 - log₁₀18
= log₁₀8 + log₁₀25 + log₁₀3² - log₁₀18      ....[ nlog_am = log_amⁿ ]
= log₁₀8 + log₁₀25 + log₁₀9 - log₁₀18
= log₁₀8 x 25 x 9 - log₁₀18             ....[ log_al + log_am + log_an = log_almn ]

= log₁₀1800 - log₁₀18         

= `log_10(1800/18)`

= `log_10 100`                       .....[ ∵ log₁₀100 = 2]
= 2