Solve the equation.
-$\log 7.06 + 3 \log x - \log x ^ { 2 } = \log 7.06 + 6$
A) $1,000,000$
B) $7,060,000$
C) $423.6$
D) 10

Question

Quizplus · Accepted Answer

Using logarithmic properties, the equation simplifies to $3 \log x - \log x^2 = 6$. This can be further simplified using the power rule ($\log a^b = b \log a$) and the quotient rule ($\log a - \log b = \log(a/b)$) to $\log x^3 - \log x^2 = 6$, which simplifies to $\log(x^3/x^2) = 6$, leading to $\log x = 6$. Since $\log x = 6$, we can rewrite this as $10^6 = x$, which means $x = 1,000,000$.

Solve the Equation log⁡7.06+3log⁡x−log⁡x2=log⁡7.06+6\log 7.06 + 3 \log x - \log x ^ { 2 } = \log 7.06 + 6log7.06+3logx−logx2=log7.06+6

Solve the Equation $\log 7.06 + 3 \log x - \log x ^ { 2 } = \log 7.06 + 6$