Solve: 6^(3n)=43^(5n-4)?

Question

a. 1.1202
b. -1.9005
c. -0.2800
d. 2.1418

HELP ME PLEASE!

Answer 1

log rules:

log(a^x) = x log(a)

first take log for both sides
log6^(3n)=log43^(5n-4)

now use the rule above:
(3n) log(6) = (5n-4) log(43)

distribute
(3n)log(6) = (5n)log(43)- 4log(43)

now subtract (5n)log(43) for both sides
(3n)log(6) - (5n)log(43)= - 4log(43)

take out n
n [3log(6) - 5log(43)] = -4log(43)

now just divide and you'll get n =~ 1.1202

Answer 2

Take the log of both sides:

3n log 6 = (5n-4) log 43

3n log 6 = 5n log 43 - 4 log 43

5n log 43 - 3n log 6 = 4 log 43

n (5 log 43 - 3 log 6) = 4 log 43

n = (4 log 43) / (5 log 43 - log 6)

Crunch this through the calculator and you'll have n.

Answer 3

6^(3n)=43^(5n-4)

3n * Ln 6 = (5n - 4) * Ln 43

3n * 1.792 = (5n - 4) * 3.761

3n = (5n - 4) * 2.099

3n = 10.496n - 8.397

-7.5n = -8.397

n = 1.1202
.

Answer 4

Take ln,
3nln6 = (5n-4)ln43
Solve for n,
n = 4ln43/(5ln43 - 3ln6) = 1.1202

Answer 5

A