Solve the following equation analytically 3ln 4x 7 15 Solv

Solve the following equation analytically. 3ln (4x + 7) = 15 Solve the following equation analytically. log_7 (x - 5) + log_7 (x + 1) = 1

Solution:

(6). 3ln(4x+7)= 15

divide by 3 on both side

ln(4x+7) = 5

Now

ln(4x+7) = lne⁵ ( ln_aa^b = b ln_aa)

4x +7 = e⁵

4x = e⁵-7

x = (e⁵-7) / 4

(15.)

log₇ (x-5) + log₇(x+1) =1

logA + logB = logAB

log₇ ((x-5) (x+1)) = 1

log₇ ((x-5) (x+1)) = log₇7¹

((x-5) (x+1)) = 7

x²-4x-5 =7

x²-4x-12 =0

(x-6) (x+2) =0

x= 6 and x=-2

Let\'s

plug x = -2 in below

log₇ (x-5) + log₇(x+1) =1

we get negative value in domain of log and that is not define

Now plug x = 2

log₇ (x-5) + log₇(x+1) =1

we can see x =6 varify above eqaution therefore

x= 6 is correct answer: