Logarithm of one
\[\log_a1=0\]
Condition
\(a\gt 0,\ a\ne1\)
NMT / ZNO
Formulas and reference
A compact mathematics reference in two levels: the NMT exam sheet and the full ZNO formula set.
NMT — exam reference sheet
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Algebra
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7 formulas
NMT mode
Shows only the compact set matching the NMT-2026 reference materials.
Exponential expressions and logarithms
Logarithms
Logarithm of the base
\[\log_a a=1\]
Condition
\(a\gt 0,\ a\ne1\)
Fundamental logarithmic identity
\[a^{\log_a b}=b\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0\)
Logarithm of a product
\[\log_a(bc)=\log_ab+\log_ac\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0,\ c\gt 0\)
Logarithm of a quotient
\[\log_a\frac bc=\log_ab-\log_ac\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0,\ c\gt 0\)
Logarithm of a power
\[\log_a b^n=n\log_a b\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0\)
Logarithm of a root
\[\log_a\sqrt[k]{b}=\frac1k\log_a b\]
Condition
\(a\gt 0,\ a\ne1,\ b\gt 0,\ k\ne0\)
No formulas match this search.
Trigonometric values table
| α | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
|---|---|---|---|---|---|---|---|---|
| sin α | \(0\) | \(1/2\) | \(\sqrt2/2\) | \(\sqrt3/2\) | \(1\) | \(0\) | \(-1\) | \(0\) |
| cos α | \(1\) | \(\sqrt3/2\) | \(\sqrt2/2\) | \(1/2\) | \(0\) | \(-1\) | \(0\) | \(1\) |
| tg α | \(0\) | \(1/\sqrt3\) | \(1\) | \(\sqrt3\) | \(\text{—}\) | \(0\) | \(\text{—}\) | \(0\) |
Squares table 10–49
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400
212 = 441
222 = 484
232 = 529
242 = 576
252 = 625
262 = 676
272 = 729
282 = 784
292 = 841
302 = 900
312 = 961
322 = 1024
332 = 1089
342 = 1156
352 = 1225
362 = 1296
372 = 1369
382 = 1444
392 = 1521
402 = 1600
412 = 1681
422 = 1764
432 = 1849
442 = 1936
452 = 2025
462 = 2116
472 = 2209
482 = 2304
492 = 2401