# Logarithm

## Log Base Calculation

The logarithm of a number to a given base is the exponent to which the base must be raised to produce the number. In mathematical terms, if 'b' is the base and 'x' is the number, then the logarithm of 'x' to the base 'b' is written as logb(x) and is defined as the exponent 'y' such that b^y = x.

The logarithm of a number to a given base is a useful tool in many areas of mathematics and science, including finance, engineering, and physics. It's also used in solving exponential equations and in graphing logarithmic functions.

In mathematics, the most common logarithms are logarithms to the base 10, which are called common logarithms, and logarithms to the base e, which are called natural logarithms. The natural logarithm is denoted by the symbol ln, and has special properties in calculus and other areas of mathematics.

To calculate any "log base of" use this fromula, which is given below-

logb(x) =
loge(x)/loge(b)
; x>0, b>1;

Where,

• b = base;
• x = value;
logb(x) Equal to
log2(4) 2
log2(8) 3
log8(3) 0.52832083357372
log2(2) 1
log2(1000) 9.9657842846621
log2(3) 1.5849625007212
log2(1) 0
log2(6) 2.5849625007212
log4(2) 0.5
log2(10) 3.3219280948874
log2(0) -INF
log2(256) 8
log2(9) 3.1699250014423
log3(7) 1.7712437491614
log10(10) 1
log4(16) 2
log5(1) 0
log10(1) 0
log2(1024) 10
log3(1) 0
log5(2) 0.43067655807339
log8(2) 0.33333333333333
log2(5) 2.3219280948874
log2(1000000) 19.931568569324
log3(9) 2
log3(27) 3
log2(32) 5
log10(0) -INF
log1(2) NAN
log4(5) 1.1609640474437
log2(16) 4
log2(2048) 11
log3(2) 0.63092975357146
log6(36) 2
log2(512) 9
log2(11) 3.4594316186373
log10(5) 0.69897000433602
log1(1) NAN
log10(100) 2
log2(12) 3.5849625007212
log4(1) 0
log2(15) 3.9068905956085
log2(10000) 13.287712379549
log3(5) 1.4649735207179
log10(1000) 3
log5(125) 3
log3(6) 1.6309297535715
log2(65536) 16
log3(3) 1
log27(9) 0.66666666666667
log2(7) 2.8073549220576
log5(3) 0.68260619448599
log8(4) 0.66666666666667
log3(4) 1.2618595071429
log4(4) 1
log3(8) 1.8927892607144
log3(10) 2.0959032742894
log5(625) 4
log2(4096) 12
log2(20) 4.3219280948874
log9(3) 0.5
log8(8) 1
log10(3) 0.47712125471966
log4(3) 0.79248125036058
log2(128) 7
log2(500) 8.9657842846621
log5(25) 2
log16(4) 0.5
log3(243) 5
log2(4000) 11.965784284662
log2(100000) 16.609640474437
log6(216) 3
log2(8192) 13
log25(5) 0.5
log5(7) 1.2090619551222
log2(100) 6.6438561897747
log4(8) 1.5
log7(49) 2
log2(50) 5.6438561897747
log7(1) 0
log2(200) 7.6438561897747
log2(40) 5.3219280948874
log2(64) 6
log16(2) 0.25
log4(7) 1.4036774610288
log16(8) 0.75
log8(20) 1.4406426982958
log3(81) 4
log4(64) 3
log4(6) 1.2924812503606
log5(10) 1.4306765580734
log5(6) 1.1132827525594
log5(8) 1.2920296742202
log10(2) 0.30102999566398
log7(9) 1.1291500681072
log3(12) 2.2618595071429
log10(4) 0.60205999132796
log5(5) 1
log2(30) 4.9068905956085
log5(50) 2.4306765580734
log3(20) 2.7268330278608
log4(20) 2.1609640474437
log4(32) 2.5
log2(25) 4.6438561897747
log10(7) 0.84509804001426
log2(255) 7.9943534368589
log3(0) -INF
log2(16384) 14
log9(81) 2
log2(32768) 15
log81(3) 0.25
log2(13) 3.7004397181411
log8(64) 2
log10(1000000) 6
log8(1) 0
log2(24) 4.5849625007212
log3(18) 2.6309297535715
log8(32) 1.6666666666667
log2(5000) 12.287712379549
log64(2) 0.16666666666667
log36(6) 0.5
log5(100) 2.8613531161468

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