To condense the expression $7 \log a + \log d$, we can use logarithmic properties. Here’s the step-by-step solution:

1. Power Rule: The logarithmic property $b \log x = \log(x^b)$ allows us to move the coefficient 7 in front of $\log a$ as an exponent of $a$. $7 \log a = \log(a^7)$

   So, the expression becomes: $\log(a^7) + \log d$

2. Product Rule: Now, using the property $\log x + \log y = \log(x \cdot y)$, we can combine the two logarithmic terms. $\log(a^7) + \log d = \log(a^7 \cdot d)$

Thus, the condensed form of the expression is: $\log(a^7 \cdot d)$

Would you like further details or have any questions on this?

Related Questions:

1. What are the main properties of logarithms used for condensing expressions?
2. How would you expand $\log(a^7 \cdot d)$ back to its original form?
3. How can you condense $5 \log x - 2 \log y + \log z$?
4. How does the power rule differ from the product rule in logarithmic operations?
5. Can the same approach be used for natural logarithms (ln)?

Tip:

Always remember the logarithmic properties: product, quotient, and power rules—these are essential for simplifying and condensing logarithmic expressions.