Solve for x

Solve for  x  .

3^7x  =  81^x+9

Since   81  =  9 * 9   and   9  =  3 * 3  ,      81  =  3 * 3  * 3 * 3  =  3⁴

3^7x  =  (3⁴)^x+9        Using the rule  (x^a)^b  =  x^ab  ......

3^7x  =  3^{4x + 36}       Now the bases are equal, so set the exponents equal.

                             We can also say this is taking the  log₃  of both sides of the equation

7x  =  4x + 36

                             Subtract  4x  from both sides.

3x  =  36

                             Divide both sides by  3 .

x  =  12

5 * 8^(4x)  =  375      divide both sides by 5

8^(4x)  = 75     take the log of both sides

log 8 ^(4x)  [ log (75)    and we can write

(4x) log (8)  = log(75)       divide both sides by  4 log (8)

x =    log (75)  /  [ 4 log (8) ]

 0.8 ⁴  =  0.4096