Algebra 2 help please show your work?

Question

Solve the following logarithmic equations showing all work.

1.
ln 7 + ln (n - 2) = ln 6n

2.
log516 - log52t = log52

3.
log5m = log5125

4.
logy = log16 + log49

5.
log6(b2 + 2) + log62 = 2

6.
log3(5x+5) - log3(x2 - 1) = 0

7. log2(x - 2) + 5 = 8 - log2 4

Answer 1

1) The given logarithmic equation is log7 + log( n -2) = log 6n

Use logarithmic formula log(a) + log(b) = log(ab)

log ( 7n - 14)  =  log ( 6n)

7n - 14 = 6n

Therefore n = 14.

 

Answer 2

4) The given logarithmic equation is logy = log16 + log49

Use logarithmic formula log(a) + log(b) = log(ab)

log(y) = log (16 (49))

y = 784

The solution is y =784.

 

Answer 3

6) The given logarithmic equation is log3(5x+5) + log3(x² - 1) = 0

Use logarithmic formula log(a) - log(b) = log(a/b)

log [3( 5x+5) / 3( x²- 1)]  = 0

 log [5( x+1)/(x+1) (x -1)] = 0

log ( 5/ ( x -1) ) = 0

elog ( 5/(x -1)) = e⁰

^{5/( x -1)  = 1}

^{Therefore  x  = 6}

^{The  solution is  x = 6.}

Answer 4

log5 16 - log5 2t = log5 2

Use logarithmic formula logc (a)  = logc (b)------>a=b

log 5 (16/2t)=log 5 2

16/2t=2

4t=16

t=4

 

Answer 5

3.

log5m = log5125.

 

Answer 6

7.

log2(x - 2) + 5 = 8 - log2 4.

Answer 7

5.
log6(b^2 + 2) + log62 = 2.