Question

Can someone please solve: Solve log ( 2x + 1 ) – log 6 = 2 for x. Please explain how you arrived at your answer.

Answer 1

Answer:

599/2

Step-by-step explanation:

$\log(2x+1)-\log(6)=2$

I'm going to use quotient rule which says: $\log(\frac{q}{p})=\log(q)-\log(p)$:

$\log(\frac{2x+1}{6})=2$

Now we are going write this in equivalent expontial form.  That is, $\log_b(a)=y$ implies $b^y=a$.

Writing in exponetial form:

$10^2=\frac{2x+1}{6}$

$100=\frac{2x+1}{6}$

Multiply both sides by 6:

$600=2x+1$

Subtract 1 on both sides:

$599=2x$

Divide both sides by 2:

$\frac{599}{2}=x$

When it comes to logarithms, you should check your solution(s).

$\log(2 \cdot \frac{599}{2}+1)-\log(6)=2$

$\log(599+1)-\log(6)=2$

$\log(600)-\log(6)=2$

$\log(\frac{600}{6})=2$

$\log(100)=2$

$2=2$

The solution checks out.

Answer 2

Answer:

x=299.5

Step-by-step explanation:

I will convert log(6) to its decimal form

$log(2x+1)-log(6)=2\\\\log(2x+1)-0.778151=2$

Step 1: Add 0.778151 to both sides.

$log(2x+1)-0.778151+0.778151=2+0.778151\\\\log(2x+1)=2.778151$

Step 2: Solve Logarithm.

$log(2x+1)=2.778151\\\\10^{log(2x+1)}=10^{102.778151}$ Take the exponent of both sides.

$2x+1=102.778151\\\\2x+1=599.999654\\\\2x+1-1=599.999654-1$

Subtract 1 from both sides.

$2x=598.999654\\\\\\\frac{2x}{2}=\frac{598.999654}{2}$

Divide both sides by 2.

$x=299.5$