Question

log 8 to the base 10 +log 25 to the base 10+ 2 log 3 to the base 10 - log 18 to the base 10​

Answer 1

Answer:

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Answer 2

Complete question: Find the value of the expression: $log_{10}8+log_{10}25+2log_{10}3-log_{10}18$.

Answer:

The value of the expression is 2.

Given,

An expression: $log_{10}8+log_{10}25+2log_{10}3-log_{10}18$.

To Find,

The value of the given expression.

Solution,

The method of finding the value of the given expression is as follows -

We know that $log_ma+log_mb=log_mab$ ,  $log_ma-log_mb=log_m(\frac{a}{b} )$,$log_ma^n=nlog_ma$, and $log_{10}10=1$.

Now we need to simplify the given expression.

$log_{10}8+log_{10}25+2log_{10}3-log_{10}18$$=log_{10}(8*25)+log_{10}3^2-log_{10}18=log_{10}(200)+log_{10}9-log_{10}18$

$=log_{10}(200)+log_{10}\frac{9}{18} =log_{10}(200)+log_{10}\frac{1}{2}$

$=log_{10}(200*\frac{1}{2} )=log_{10}(100 )=log_{10}10^2$

$=2log_{10}10=2*1=2$

Hence, the value of the expression is 2.

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