Question

solve this question:--→ Find the value of x, if 2log3 + 3log5 - 4log2 = logx​

Answer 1

2log3+3log5+5log2

We know that, logx

y

=ylogx,

Using the above property we can reduce the given equation as,

=log3

2

+log5

3

+log2

5

=log9+log125+log32

also, logx+logy+logz=logxyz, hence we can write the above as,

=log(9×125×32)

=log(36000)

∴ 2log3+3log5+5log2 can be written as a single logarithm as log36000.

Answer 2

Solution

2log3+3log5+5log2

We know that, logxy=ylogx,

Using the above property we can reduce the given equation as,

=log32+log53+log25

=log9+log125+log32

also, logx+logy+logz=logxyz, hence we can write the above as,

=log(9×125×32)

=log(36000)

∴    2log3+3log5+5log2 can be written as a single logarithm as log36000