Find the missing number. Round to the nearest hundredth if necessary.
-$13 ^ { ? } = 19$
A) $1.38$
B) $0.87$
C) $1.15$
D) $1.46$

Question

Quizplus · Accepted Answer

We can use logarithms to solve for the missing number. Taking the logarithm of both sides to the base 13, we get:

$$\log_{13}(13^x) = \log_{13}(19)$$

Simplifying the left side using the logarithmic identity, we get:

$$x = \log_{13}(19) \approx 1.15$$

Therefore, the closest answer choice is C, $1.15$, rounded to the nearest hundredth.

Find the Missing Number 13?=1913 ^ { ? } = 1913?=19