Question

please solve this

Log 49√7 + log 25√5 + log 4√2

Answer 1

☆your Question:-

Log 49√7 + log 25√5 + log 4√2

☆your Answer:-

log497+log255−log42

=log10175log72.71/2+log52.51/2−log22.21/2

=log35/2log75/2+log55/2−log25/2

=25log35/2[log7+log5−log2]=25.log35/2log235

=25 

☆ THANK YOU ☆

Answer 2

Given:

An expression in logarithmic form log 49√7 + log 25√5 + log 4√2.

To Find:

The value of the expression after simplification.

Solution:

The given problem can be solved using the properties of logarithms.

1. The given expression is log49√7 + log 25√5 + log 4√2.

2. The above expression can be further simplified as,

=> log49√7 + log 100√10, (log a + log b = log(ab)).

=> log49√7 + log 100 + log√10, (log (ab)= log a + log b)

=> log49√7 + log $10^2$ + log $10^\frac{1}{2}$,

=> log $7^\frac{3}{2}$+ 2 + 1/2, (log $x^2$ = 2 log x),

=> 3/2 (log 7) + 5/2,

=> 3/2 (0.845) + 2.5, ( Substituting the value of log7 as 0.845).

=> 1.5(0.845) + 2.5,

=> 1.2675 + 2.5,

=> 3.7675.

Therefore, the value of the expression log49√7 + log 25√5 + log 4√2 is 3.7675.