The algebra logarithms solve represents the problems in logarithms that uses the algebra. The logarithm for the given number to a given base is generally the power or exponent to which the base must be raised in order to produce that number.Sometimes the logarithmic table are used in the problems for evaluating the values in the forms of logarithmic algebra.
Examples to explain algebra logarithms solve
solve the natural logarithm for ln ((ab)2/ca)
solution:
ln ((ab)2/ca)
=ln ((ab)2) - ln (ca) by property Quotient formula
=ln a2 + ln b2 - (ln c+ ln a) by property Product formula
=2 ln a + 2 ln b- ln c- lna
= ln a + 2 ln b - ln c
Consider the same problem without using natural logarithms.
solve log ((ab)2/ca)
=log ((ab)2) - log (ca) by property Quotient formula
=log a2 + log b2 - (log c+ log a) by property Product formula
=2 log a + 2 log b- log c- log a
= log a + 2 log b - log c
solve the following log x expansions for logarithmic algebra log1213 + 13 log2222
Given:
log12 13 + 13 log22 22
= log1213 + 13 (1) ( log aa = 1)
= log1213 + 13
This is the required log x expansion. Hence we solved the problem.
Problems to explain algebra logarithms solve
Solve log51003
Solution:
log51003=3 log5100
= 3 log5(10*10)
= 3 (log510 + log510)
= 3(2 log510)
Log51003= 6 log510.
Solve the following log x expansions for logarithmic algebra log17y - log17 x + log1715
Solution:
log17 y - log17 x + log17 15 (given)
= log17`(y / x)` + log17 15 ( log a - log b = log `a/b` )
= log17( `y/x` . 15) (log a + log b = log a.b)
This is the required log x expansion. Hence we solved the above problem.
Prove that log3 4 x log4 5 x log5 6 x log6 7 x log7 8 x log8 9 = 2
Solution:
Left Hand Side = ( log3 4 x log4 5 ) x ( log5 6 x log6 7 ) x ( log7 8 x log8 9 )
=log3 5 x log5 7 x log7 9
= log3 5 x ( log5 7 x log7 9)
= log3 5 x log5 9
= log3 9 = log3 32
= 2log3 3
= 2 x 1
= 2 = Right Hand Side
This problem explains the change of base rule.
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