Example 11:

Expand log 343/125

solution:

As you know,log_ax/y=log_ax- log_ay

so,log 343/125=log 343-log 125

=log 7³-log 5³

=3 log 7- 3log 5

(since,log_ax ⁿ=m log_ax)

So log 343/125 =3 ( log 7- log 5)

Example 12:

write 2 log 3 + 3 log 5- 5 log 2 as a single logarithm

solution:

2 log 3 + 3 log 5 - 5 log 2

=log 3 ²+ log 5 ³ - log 2 ⁵

(since in n log a x=log_axⁿ)

= log 9+ log 125- log 32

=log (9×125)- log 32

(since log^ax+ log ^a y= log^axy)

=log 1125- log 32

=log 1125/32( since log^ax - log^ay=log a x/y)



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