Topic:-Logarithms
The logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.
For example, the logarithm of 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 103 = 1000, so log101000 = 3, and 25 = 32, so log232 = 5.
Let's see a problem on logarithms.
Question:-
solve 6x+5=3x-4
Answer:-
The logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.
For example, the logarithm of 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 103 = 1000, so log101000 = 3, and 25 = 32, so log232 = 5.
Let's see a problem on logarithms.
Question:-
solve 6x+5=3x-4
Answer:-
Given 6x+5=3x-4
log 6 x+5=log 3x-4
(x+5)log6 = (x-4)log3
xlog6+5log6 = xlog3-4log3
xlog6-xlog3= -4 log3-5log6
x[log6-log3]= -[4log3+5log6]
xlog 6/2 = -[log 34+log65]
xlog3= -log34*65
-log(34*65)
x= -----------------
log3
x=-log3(34*65)
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