To solve the inequality log7 (x-1) ≤ log7 2 + log7 3, we can use the properties of logarithms.
First, we can combine the logarithms on the right side of the inequality:
log7 2 + log7 3 = log7 (2*3) = log7 6
So the inequality becomes:
log7 (x-1) ≤ log7 6
Next, we can remove the logarithms by converting them to exponential form:
7^(log7 (x-1)) ≤ 7^(log7 6)
This simplifies to:
x-1 ≤ 6
Now we can solve for x:
x ≤ 7
Therefore, the solution to the inequality log7 (x-1) ≤ log7 2 + log7 3 is x ≤ 7.
To solve the inequality log7 (x-1) ≤ log7 2 + log7 3, we can use the properties of logarithms.
First, we can combine the logarithms on the right side of the inequality:
log7 2 + log7 3 = log7 (2*3) = log7 6
So the inequality becomes:
log7 (x-1) ≤ log7 6
Next, we can remove the logarithms by converting them to exponential form:
7^(log7 (x-1)) ≤ 7^(log7 6)
This simplifies to:
x-1 ≤ 6
Now we can solve for x:
x ≤ 7
Therefore, the solution to the inequality log7 (x-1) ≤ log7 2 + log7 3 is x ≤ 7.