Use algebraic procedures to find the exact solution(s) of the equation below. $10 ^ { 3 - x } = 370$
A) $x = 1 + 3 \log 370$
B) $x = - 1 - 3 \log 370$
C) $x = - 1 + 3 \log 370$
D) $x = - 3 - \log 370$
E) $x = 3 - \log 370$

Question

Quizplus · Accepted Answer

To solve $10 ^ { 3 - x } = 370$, we first take the logarithm of both sides: $\log(10 ^ { 3 - x }) = \log(370)$. Using the property of logarithms that allows us to bring the exponent down ($\log(a^b) = b\log(a)$), we get $(3 - x)\log(10) = \log(370)$. Since $\log(10) = 1$, this simplifies to $3 - x = \log(370)$. Solving for $x$, we get $x = 3 - \log(370)$, which matches choice E.

Use Algebraic Procedures to Find the Exact Solution(s) of the Equation