Question

solve the equation for x. give an exact answer and a four - decim
log(2x - 2)=-0.9
the exact answer is x =
(simplify your answer.)

Explanation:

Step1: Rewrite in exponential form

If $\log(2x - 2)=- 0.9$, and assuming base - 10 logarithm, then $10^{\log(2x - 2)}=10^{-0.9}$ by the property $a^{\log_a(b)}=b$. So, $2x-2 = 10^{-0.9}$.

Step2: Solve for $x$

First, add 2 to both sides of the equation: $2x=10^{-0.9}+2$. Then divide both sides by 2: $x=\frac{10^{-0.9}+2}{2}$.

Step3: Calculate the four - decimal answer

We know that $10^{-0.9}=\frac{1}{10^{0.9}}\approx\frac{1}{7.9433}=0.1259$. Then $x=\frac{0.1259 + 2}{2}=\frac{2.1259}{2}=1.06295\approx1.0630$.
The exact answer is $x=\frac{10^{-0.9}+2}{2}$.

Answer:

The exact answer is $x=\frac{10^{-0.9}+2}{2}$; Four - decimal answer: $x\approx1.0630$