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fredd [130]
3 years ago
7

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

Mathematics
2 answers:
damaskus [11]3 years ago
7 0

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.

MrMuchimi3 years ago
7 0

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

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