We are given the equation $8^5 = x$ and need to find the equivalent logarithmic form from the provided options.

Step-by-step:

The general rule for converting an exponential equation $a^b = c$ into logarithmic form is: $\log_a(c) = b$ Here, the base is $8$, the exponent is $5$, and the result is $x$. Using the formula, we get: $\log_8(x) = 5$

Now, let's look for the matching equation in the options:

• Option (a): $\log_x(8) = 5$ (Not correct; the base and argument are switched)
• Option (b): $\log_5(x) = 8$ (Not correct; wrong base and argument)
• Option (c): $\log_5(8) = x$ (Not correct; wrong base)
• Option (d): $\log_8(x) = 5$ (Correct; matches our equation)
• Option (e): $\log_5(5) = x$ (Not correct; wrong base and argument)
• Option (f): $\log_x(5) = 8$ (Not correct; wrong base and argument)

Correct answer: (d) $\log_8(x) = 5$

Would you like more details or further clarification?

Related Questions:

1. How do you convert logarithmic equations to exponential form?
2. What is the difference between a logarithmic and an exponential equation?
3. How do you evaluate logarithms without a calculator?
4. How can we use logarithmic properties to simplify equations?
5. What are some real-world applications of logarithmic functions?

Tip:

Always remember that the base of the logarithm corresponds to the base of the exponent when converting between exponential and logarithmic forms.