Solve the equation and express the solution in exact form.
-$$\log ( x + 10 ) = 1 + \log ( 4 x - 3 )$$
A) $\{ 1 \}$
B) $\left\{ \frac { 40 } { 39 } , 1 \right\}$
C) $\left\{ \frac { 13 } { 3 } \right\}$
D) $\left\{ \frac { 40 } { 39 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $\log ( x + 10 ) = 1 + \log ( 4 x - 3 )$, we first use the property that $\log a = \log b$ implies $a = b$, and the fact that $1 = \log 10$ (since we're dealing with base 10 logarithms by default). Thus, we can rewrite the equation as $\log ( x + 10 ) = \log ( 10 \cdot ( 4 x - 3 ) )$, which simplifies to $x + 10 = 40x - 30$. Solving for $x$, we get $39x = 40$, or $x = \frac{40}{39}$.

Solve the Equation and Express the Solution in Exact Form log⁡(x+10)=1+log⁡(4x−3)\log ( x + 10 ) = 1 + \log ( 4 x - 3 )log(x+10)=1+log(4x−3)

Solve the Equation and Express the Solution in Exact Form $\log ( x + 10 ) = 1 + \log ( 4 x - 3 )$