Final answer:
The logarithmic expression equivalent to log₈₁9 is log₁₆₉.
Step-by-step explanation:
The given expression is log₈19. In this expression, the base is 8 and the number inside the logarithm is 9. To find an equivalent logarithmic expression, we need to rewrite 9 in terms of the base 8. Since 8 raised to what power equals 9?
81 = 8
82 = 64
We can see that 8 raised to the power of 2 is greater than 9, and 8 raised to the power of 1 is less than 9. Therefore, the equivalent logarithmic expression is log₈19 = log₁89.