Question

Write the equation in its equivalent exponential form. Then solve for x.
Log3 x = -4

Answer 1

The logarithmic equation Log3 x = -4 can be rewritten in its exponential form as 3^-4 = x, which simplifies to x = 1/81.

Step-by-step explanation:

To write the logarithmic equation Log3 x = -4 in its equivalent exponential form, we apply the definition of a logarithm. The base of the logarithm becomes the base of the power, the right side of the logarithmic equation becomes the exponent, and the argument of the logarithm (x) becomes the result of the power. Thus, the equivalent exponential form is 3-4 = x.

Next, we solve for x.

• 3-4 means 1 divided by 3 raised to the 4th power, which is:
• 1 / (3 * 3 * 3 * 3) = 1 / 81.
• Therefore, x = 1/81.