Solve each of the following equations: A) 3 = log2(1/y) B) log(x + 3) + log x = 1 C) log(x + 2)-?

Question

Solve each of the following equations:
A) 3 = log2(1/y)
B) log(x + 3) + log x = 1
C) log(x + 2) - log5(x - 1) = 2 log 5 to the power of 3
D) log(35 - x3) / log (5 - x) = 3

Answers:
A)1/8
B) 2
C) 11/8
D) 3 or 2


Please show your work. Thank you

Answer 1

A) 3 = log2(1/y)
<=> 2^3 = 1/y
<=> 8 = 1/y
<=> y = 1/8

B) log(x + 3) + log x = 1
<=> log ((x+3) x) = 1, x > 0
<=> x(x+3) = 10
<=> x^2 + 3x - 10 = 0
<=> (x - 2) (x + 5) = 0
<=> x = 2 or -5, but x > 0 so x = 2.

C) log(x + 2) - log5(x - 1) = 2 log 5 to the power of 3
I think you've mistyped this. I think it should be
log5 (x+2) - log5 (x-1) = 2 log5 3
<=> log5 ((x+2) / (x-1)) = log5 (3^2)
<=> (x+2) / (x-1) = 9
<=> x + 2 = 9x - 9
<=> 8x = 11
<=> x = 11/8.

D) log(35 - x^3) / log (5 - x) = 3
<=> log (35-x^3) = 3 log (5-x)
<=> log (35-x^3) = log ((5-x)^3)
<=> 35 - x^3 = (5-x)^3 = 125 - 75x + 15x^2 - x^3
<=> x^2 - 5x + 6 = 0
<=> (x - 2) (x - 3) = 0
<=> x = 2 or 3.

Answer 2

qwdcs