SOLUTION: Use logs on both sides of the equation 9^28 - 9^27 / 8 = 3^x to find the unknown Please show all steps The 8 is dividing (9^28 - 9^27)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Use logs on both sides of the equation 9^28 - 9^27 / 8 = 3^x to find the unknown Please show all steps The 8 is dividing (9^28 - 9^27)      Log On


   

Question 133258: Use logs on both sides of the equation
9^28 - 9^27 / 8 = 3^x to find the unknown
Please show all steps
The 8 is dividing (9^28 - 9^27)
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given : %289%5E28+-+9%5E27%29+%2F+8+=+3%5Ex+
%289%5E27%289-1%29%29%2F8+=+3%5Ex
%289%5E27%288%29%29%2F8+=+3%5Ex
9%5E27+=+3%5Ex
3%5E3%5E27=+3%5Ex
3%5E81=+3%5Ex
x = 81

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%289%5E28+-+9%5E27%29+%2F+8+=+3%5Ex+ Start with the given equation


%289%5E%2827%2B1%29+-+9%5E27%29+%2F+8+=+3%5Ex+ Rewrite 9%5E28 into 9%5E%2827%2B1%29



%289%5E27%2A9%5E1-+9%5E27%29+%2F+8+=+3%5Ex+ Break up 9%5E%2827%2B1%29 into 9%5E27%2A9%5E1 through the identity x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez


%289%5E27%289%5E1-+1%29%29+%2F+8+=+3%5Ex+ Factor out the GCF 9%5E27


%289%5E27%289-+1%29%29+%2F+8+=+3%5Ex+ Evaluate 9%5E1 to get 9


%289%5E27%288%29%29+%2F+8+=+3%5Ex+ Subtract


%289%5E27cross%288%29%29+%2F+cross%288%29+=+3%5Ex+ Cancel like terms


9%5E27+=+3%5Ex+ Simplify


%283%5E2%29%5E27+=+3%5Ex+ Rewrite 9 as 3%5E2


3%5E%282%2A27%29+=+3%5Ex+ Multiply the exponents. Remember, %28x%5Ey%29%5Ez=x%5E%28y%2Az%29


3%5E54+=+3%5Ex+ Multiply


Since the bases are equal, the exponents are equal. So this means that x=54