Respuesta :

㏒₆₄(0.5) = x
        64ˣ = 0.5
  ㏑(64ˣ) = ㏑(0.5)
 x㏑(64) = ㏑(0.5)
  x㏑(2⁶) = ㏑(2⁻¹)
 6x㏑(2) = -㏑(2)
  6㏑(2)     6㏑(2)
           x = ⁻¹/₆

The solution of the logarithmic equation will be negative one-sixth, that is - 1/6.

What is a logarithm?

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

The logarithmic equation is given below.

log₆₄ 0.5 = x

Then the value of the variable x will be

Taking anti-log, then the logarithmic equation will be

64ˣ = 0.5

Taking natural log on both side, then the equation will be

  ln64ˣ) = ln(0.5)

Simplify the logarithmic equation, then the equation will be

x ln 64 = ln (1/2)

x ln (2⁶) = ln (2⁻¹)

6x ln(2) = - ln(2)

        6x = –1

          x = –1/6

The solution of the logarithmic equation will be negative one-sixth, that is - 1/6.

More about the logarithm link is given below.

https://brainly.com/question/7302008

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