SOLUTION: I'm new to logs and I'm not sure how to answer these questions: (any help would be greatly appreciated, thanks :D ) 1) log(base4) (x^2

SOLUTION: I'm new to logs and I'm not sure how to answer these questions: (any help would be greatly appreciated, thanks :D ) 1) log(base4) (x^2 - 3) + log(base 4) 10 = 1 2) log(base

Question 309405: I'm new to logs and I'm not sure how to answer these questions:
(any help would be greatly appreciated, thanks :D )
1) log(base4) (x^2 - 3) + log(base 4) 10 = 1
2) log(base 5)3 - log(base 5) 5x = 2
3) ln (x+7) + ln (x+3) = ln 77
4) ln (x+2) - ln (x-1) = 1

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1) log(base4) (x^2 - 3) + log(base 4) 10 = 1
addition of logs is the same as multiply so we can write it:
log4(10*(x^2-3)) = 1
log4(10x^2 - 30) = 1
Write the exponent equiv of logs
4^1 = 10x^2 - 30
4 = 10x^2 - 30
4 + 30 = 10x^2
34 = 10x^2
x^2 = 34/10
x^2 = 3.4
x =
x = 1.844
:
2) log(base 5)3 - log(base 5) 5x = 2
subtracting logs is the same as divide so we can write it

exponent equiv
5^2 =
25 =
Multiply by 5x
25(5x) = 3
125x = 3
x =
:
:
3) ln (x+7) + ln (x+3) = ln 77
ln((x+7)*(x+3)) = ln(77)
FOIL
ln((x^2+10x+21) = ln(77)
same as
x^2 + 10x + 21 = 77
x^2 + 10x + 21 - 77 = 0
A quadratic equation
x^2 + 10x - 56 = 0
Factors to
(x-14)(x-4) = 0
only the positive solution can be used here
x = 4
:
4) ln (x+2) - ln (x-1) = 1

find the e^ of both sides
= 2.71828
x + 2 = 2.71828(x-1)
x + 2 = 2.71828x - 2.71828
2.71828 + 2 = 2.71828x - x
4.71828 = 1.71828x
x = 4.71828/1.71828
x = 2.746

RELATED QUESTIONS
log(7)x=5 the answer I got is x=16,954 and also log x =1 the answer I got is x=10 (answered by Theo)

The problem states to solve. 4/(m^2-7) = 1 I came up with m = + or - sqrt of 11. (answered by edjones)

Divide the first polynomial by the second. 6x^3-19x^2+x=6 and x-3 I am not sure how to (answered by vleith)

The Majik car rental company charges a flat fee of $21 per day and a mileage charge of... (answered by Hook)

Hi, I'm really not sure how to solve this problem. log(2x)=log(x+70) Each log has base... (answered by Alan3354)

Hey, Quick question. I have the following problem: Using properties of logarithms,... (answered by asuar010,solver91311)

Hello, I am having trouble answering two questions on projectiles using formulas: d=16t^2 (answered by solver91311,ikleyn,josmiceli)

35m=____mi, given 1.00km=0.621mi My teacher wants it set up where everything cancels... (answered by MathTherapy,lwsshak3)

Use the change of base formula to convert log_6(7) to a ratio of logs base 8 _means... (answered by MathLover1)