Final answer:
To write the expression log₇√x - log₇⁸ as a single logarithm, we can use the property that the logarithm of a quotient is equal to the difference of the logarithms. So, the expression can be written as log₇((x^(1/2))/(⁸)).
Step-by-step explanation:
To write the expression log₇√x - log₇⁸ as a single logarithm, we can use the property that the logarithm of a quotient is equal to the difference of the logarithms. So, we have:
log₇(√x/⁸)
Next, we can simplify the expression by combining the radical and the exponent. Remember that the square root (√) is the same as raising to the power of (1/2), and the exponent can be written as a factor. Therefore, the expression becomes:
log₇((x^(1/2))/(⁸))
Answer: log₇((x^(1/2))/(⁸))