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Evaluating Logarithms Without a Calculator
Condense Into a Single Logarithm
Solving Equations:
Log = Log
Solving Equations:
Log = Number
Solving Equations:
Exponential
100
log_4 (2) =
1/2 or 0.5
100
3 log_6 (m) - 1/2 log_6 (n)
log_6 (m^3 / sqrt(n))
100
log_7 (9x-4) = log_7 (x+20)
x = 3
100
log_4 (5m+9) = 3
m = 11
100
25^(v-2) = 625
v = 4
200
log_5 (625)
4
200
log (3) + log (20) - log (4)
log (15)
200
log_5 (m^2 - 12) = log_5 (m)
m = 4, m = -3 is extraneous
200
log_36 (20-4p) = 1/2
p = 7/2 or 3 1/2 or 3.5
200
8^k = 78
k = log (78) / log(8) = 2.0951
300
log_4 (1/64)
-3
300
log_3 (x) + log_3 (x-4)
log_3 (x^2 - 4x)
300
log_3 (4) + log_3 (a+5) = log_3 (56)
a = 9
300
log_6 (7k-1) = 3
k = 31
300
15^(3a) + 7 = 67
a = [ log (60) / log (15) ] / 3 = 0.5040
400

log_2 (4 sqrt(2))

2

400
3 log_7 (x^2) + 4 log_7 (y^3)
log_7 (x^6 y^12)
400
log (2y - 10) = 7 log (2) - log (8)
y = 13
400
log (n+8) + log (4) = 2
n = 17
400
14^(3-8x) + 9 = 77
x = { [ log (68) / log (14) ] - 3 } / -8 = 0.1751
500
log (1000)
3
500
5 log (M) - log (M^2)
log (M^3)
500
log_4 (108) - log_4 (9) = log_4 (7a-9)
a = 3
500
2 log_3 (x) - log_3 (x-2) = 2
x = 3 and x = 6
500
2 * 18^(10r-3) - 1 = 73
r = { [ log (37) / log (18) ] + 3 } / 10 = 0.4249