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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.

Urugero · 2^x = 8

Algebra · Exponential-Equations

Solve 2^x = 8

2^{x} = 8

ku

  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.

i
x = 3

Guhitamo A, Cyangwa Ubwoko: Cyangwa Gushushanya. Intera, A Ishusho, i Gihishwe & Kugeza & Kubaza.

Kuri Gushyiraho

A Kigenga Konti: & OYA & Ongera Ibisobanuro: ku, A Ibijyana Bya, in Rimwe, na A Kubaza Bigyanye iyi Ipaji:. Imibare ni Gufungura Kuri, in Cyangwa OYA.

Kwiyandikisha Ifashayinjira

Byakoreshejwe

Icyo ari cyo cyose Ibimenyetso ya: i Byuzuye Insobanuro:, A Ishusho, na buri Ibaruwa: in.

Kuri: 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.

Abaturage

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.

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