maths.free › Algebra › Exponential and logarithmic equations

Exponential and logarithmic equations

Undo an exponential with a logarithm, and a logarithm with an exponential.

When the unknown is in the exponent, take a logarithm of both sides; the exponent comes down as a multiplier. When the unknown is inside a log, rewrite in exponential form. Always check the domain: logarithms need positive arguments.

Arbejdstxrd eksempel · 2^x = 8

Algebra · Exponential-Equations

Solve 2^x = 8

2^{x} = 8

Trin for trin

  1. 2^{x} = 8

    Start from the equation as given.

  2. 2^{x} - 8 = 0

    Bring everything to one side.

  3. 2^{x} - 8 = 0

    Isolate the exponential, then take a logarithm of both sides.

  4. x = 3

    Solve for the variable.

Afslør svaret
x = 3

Nu er du Vælg et problem, eller skriv eller tegne din egen. Hvert skridt, et billede, svaret skjult, indtil du spørger.

Fortsæt med at arbejde

En gratis konto tilføjer noter om hver lektion, en rekord over, hvad du har afsluttet, dine løste problemer på ét sted, og en vejleder, du kan spørge om denne side. Matematik selv er åben for alle, logget på eller ej.

Tilmeld dig Login

Symboler brugt her

Tryk på ethvert symbol for den fulde definition, et billede, og hvad hvert bogstav i det betyder.

Hvordan: Exponential and logarithmic equations

  1. Start from the equation as given.
  2. Bring everything to one side.
  3. Isolate the exponential, then take a logarithm of both sides.
  4. Solve for the variable.

Spørgsmål folk spørger

What does it mean to solve an equation?

To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.

Why do I sometimes get two answers?

A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.

How do I know whether to factor or use the quadratic formula?

Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.

Mere i Algebra

Linear equationsQuadratic equationsSystems of equationsInequalitiesFactoringExpandingSimplifying expressionsFunctions and graphsPolynomial equationsAbsolute value