SOLUTION: Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. ((x-6))/(8^(10))=\sqrt(8)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. ((x-6))/(8^(10))=\sqrt(8)      Log On


   

Question 1061943: Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.
((x-6))/(8^(10))=\sqrt(8)
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.
Assuming the equation is:
%28%28x-6%29%29%2F%288%5E%2810%29%29+=+sqrt%288%29
multiply both sides by 8^10
%28x+-+6%298%5E-10+=+sqrt%288%29
we can write the square root as an exponent
%28x+-+6%29+%2A+8%5E-10+=+8%5E%281%2F2%29
divide both sides by 8^-10
x+-+6+=+8%5E%281%2F2%29%2F8%5E-10
which is
x+-+6+=+8%5E%281%2F2%29%2A8%5E10
add the exponents
x+-+6+=+8%5E10.5
calculates to
x - 6 = 3037000500
x = 3037000506



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.
((x-6))/(8^(10))=\sqrt(8)
%28x+-+6%29%2F8%5E10+=+sqrt%288%29

%28x+-+6%29%2F8%5E10+=+matrix%282%2C1%2C+%22+%22%2C+8%5E%281%2F2%29%29 ------ Changing matrix%281%2C3%2C+sqrt%288%29%2C+to%2C+matrix%282%2C1%2C+%22+%22%2C+8%5E%281%2F2%29%29%29

x+-+6+=+8%5E10+%2A+matrix%282%2C1%2C+%22%22%2C+8%5E%281%2F2%29%29 --- Cross-multiplying