{
  "unit": 7,
  "title": "Logarithmic Functions & Equations",
  "terms": [
    {
      "en": "logarithm",
      "es": "logaritmo",
      "fr": "logarithme",
      "ar": "لوغاريتم",
      "pt": "logaritmo",
      "definition": "The exponent y satisfying b^y=x for base b>0 and b≠1 and argument x>0."
    },
    {
      "en": "inverse of exponential",
      "es": "inversa de la exponencial",
      "fr": "réciproque de l'exponentielle",
      "ar": "معكوس الدالة الأسية",
      "pt": "inversa da exponencial",
      "definition": "The logarithm reverses exponentiation with the same valid base."
    },
    {
      "en": "exponential form",
      "es": "forma exponencial",
      "fr": "forme exponentielle",
      "ar": "الصيغة الأسية",
      "pt": "forma exponencial",
      "definition": "The equality b^y=x equivalent to log_b(x)=y."
    },
    {
      "en": "common logarithm",
      "es": "logaritmo decimal",
      "fr": "logarithme décimal",
      "ar": "اللوغاريتم العشري",
      "pt": "logaritmo decimal",
      "definition": "A logarithm with base ten, commonly written log(x) in algebra courses."
    },
    {
      "en": "natural logarithm",
      "es": "logaritmo natural",
      "fr": "logarithme népérien",
      "ar": "اللوغاريتم الطبيعي",
      "pt": "logaritmo natural",
      "definition": "A logarithm with base e, written ln(x)."
    },
    {
      "en": "logarithmic base",
      "es": "base logarítmica",
      "fr": "base du logarithme",
      "ar": "أساس اللوغاريتم",
      "pt": "base logarítmica",
      "definition": "The positive number b other than 1 used in log_b(x)."
    },
    {
      "en": "product rule for logs",
      "es": "regla del producto de logaritmos",
      "fr": "règle du produit des logarithmes",
      "ar": "قاعدة ضرب اللوغاريتمات",
      "pt": "regra do produto dos logaritmos",
      "definition": "For positive a and c, log_b(ac)=log_b(a)+log_b(c)."
    },
    {
      "en": "quotient rule for logs",
      "es": "regla del cociente de logaritmos",
      "fr": "règle du quotient des logarithmes",
      "ar": "قاعدة قسمة اللوغاريتمات",
      "pt": "regra do quociente dos logaritmos",
      "definition": "For positive a and c, log_b(a/c)=log_b(a)-log_b(c)."
    },
    {
      "en": "power rule for logs",
      "es": "regla de la potencia logarítmica",
      "fr": "règle de puissance des logarithmes",
      "ar": "قاعدة قوة اللوغاريتم",
      "pt": "regra da potência dos logaritmos",
      "definition": "For a>0, log_b(a^k)=k log_b(a)."
    },
    {
      "en": "logarithmic solution",
      "es": "solución logarítmica",
      "fr": "solution logarithmique",
      "ar": "حل لوغاريتمي",
      "pt": "solução logarítmica",
      "definition": "Solving an exponential equation by applying a logarithm."
    },
    {
      "en": "exponential equation",
      "es": "ecuación exponencial",
      "fr": "équation exponentielle",
      "ar": "معادلة أسية",
      "pt": "equação exponencial",
      "definition": "An equation with a variable in an exponent."
    },
    {
      "en": "logarithmic equation",
      "es": "ecuación logarítmica",
      "fr": "équation logarithmique",
      "ar": "معادلة لوغاريتمية",
      "pt": "equação logarítmica",
      "definition": "An equation containing one or more logarithmic expressions."
    },
    {
      "en": "logarithmic domain",
      "es": "dominio logarítmico",
      "fr": "domaine logarithmique",
      "ar": "مجال اللوغاريتم",
      "pt": "domínio logarítmico",
      "definition": "Real logarithm arguments must be strictly positive."
    },
    {
      "en": "change of base",
      "es": "cambio de base",
      "fr": "changement de base",
      "ar": "تغيير الأساس",
      "pt": "mudança de base",
      "definition": "The identity log_b(x)=ln(x)/ln(b) for valid b and x."
    },
    {
      "en": "base ten",
      "es": "base diez",
      "fr": "base dix",
      "ar": "الأساس عشرة",
      "pt": "base dez",
      "definition": "The base of common logarithms and the decimal number system."
    },
    {
      "en": "calculator logarithm",
      "es": "logaritmo en calculadora",
      "fr": "logarithme à la calculatrice",
      "ar": "حساب اللوغاريتم آلياً",
      "pt": "logaritmo na calculadora",
      "definition": "Evaluating a logarithm numerically, checking base and argument."
    },
    {
      "en": "logarithmic scale",
      "es": "escala logarítmica",
      "fr": "échelle logarithmique",
      "ar": "مقياس لوغاريتمي",
      "pt": "escala logarítmica",
      "definition": "A scale where equal distances correspond to equal multiplicative ratios."
    },
    {
      "en": "logarithmic data interpretation",
      "es": "interpretación de datos logarítmicos",
      "fr": "interprétation de données logarithmiques",
      "ar": "تفسير البيانات اللوغاريتمية",
      "pt": "interpretação de dados logarítmicos",
      "definition": "Reasoning about multiplicative differences represented on a log scale."
    }
  ],
  "schema_version": "1.1"
}