SOLUTION: Solve each equation for x A. 27^X=3^X+1 B. e^3x-1=12 C.log(x+3)-log x=log 2 D.log5 X+ 2log5 X=3 E.ln(X+5)-ln 3=0

Question 166638: Solve each equation for x
A. 27^X=3^X+1
B. e^3x-1=12
C.log(x+3)-log x=log 2
D.log5 X+ 2log5 X=3
E.ln(X+5)-ln 3=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started.

A)

Start with the given equation

Rewrite as

Multiply the exponents.

Since the bases are equal, this means that the exponents are equal

Set the exponents equal to one another.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

----------------------------------------------------------------------

Answer:

So the answer is which in decimal form is .

B)

Start with the given equation

Take the natural log of both sides to eliminate the base "e"

Add 1 to both sides.

Divide both sides by 3 to isolate "x"

So the answer is which approximates to 1.16164
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