Properties of Logarithms
Use log 4 = 0.602 and log 12= 1.079 to evaluate the logarithm:
log 3
log 12- log 4 = 1.079- 0.602
= 0.477
Expand the expression:
log3 4x
= log3 4 + log3 x
Use the change of base formula to evaluate the logarithm:
log4 7
= 1.404
Solve:
8x = 20
= 1.44
Solve this logarithmic equation:
log5 (4x - 7) = log5 (x + 5)
= x = 4
Which logarithm has the same value as the expression: ln 6 + ln 2?
A. ln 64 C. ln 12
B. ln 3 D. ln 36
C. ln 12
Expand the expression:
log2 2/5
= log2 2 - log2 5
Use the change of base formula to evaluate the logarithm:
log5 14
= 1.640
Solve:
e-x = 5
= -1.61
Exponentiate each side of an equation:
log4 (5x - 1) = 3
= x = 13
Use log 4 = 0.602 and log 12= 1.079 to evaluate the logarithm:
log 48
log 12 + log 4 = 1.079 + 0.602
= 1.681
Expand the Expression:
log7 5x3yz2
= log7 5 + 3 log7 x + log7 y + log7 z2
Use the change of base formula to evaluate the logarithm:
log6 24/5
=0.875
Solve:
73x = 18
= 0.5
What is (are) the solution (s) of
log 2x + log (x - 5) = 2?
A. -5, 10 C. 10
B. 5 D. 5, 10
A. x = 10 or x = -5
Use log 4 = 0.602 and log 12= 1.079 to evaluate the logarithm:
log 1/3
log 4/12 = log 4 - log 12 = 0.602 - 1.079
= -0.477
Expand the expression:
ln 6x2/y4
= ln 6 + 2 ln x - 4 ln y
Use the change of base formula to evaluate the logarithm:
log3 9/40
= -1.358
76x = 12
= 0.21
Solve by equating exponents:
4x = (1/2) x-3
x = 1
Use log 4 = 0.602 and log 12= 1.079 to evaluate the logarithm:
log 64
log 43 = 3 log 4 = 3(0.602)
= 1.806
Expand the expression:
log3 √ 9x
log3 3 + 1/2 log3x
Use the change of base formula to evaluate the logarithm:
log7 3/16
=-0.860
103x + 4 = 9
= 0.23