SOLUTION: Solve the following exponential equation. 2^x2 * 5^7x=625 The​ solution(s) is/are ?

Algebra.Com
Question 1039588: Solve the following exponential equation.
2^x2 * 5^7x=625
The​ solution(s) is/are ?
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the following exponential equation.
2^x2 * 5^7x=625
The​ solution(s) is/are ?
-----------
Is the exponent of 2 x? Or 2x?
Is the exponent of 5 7? or 7x?
-----
Parentheses are free.
Use some.
-------
The​ solution(s) is/are ?
--
This is not needed.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

I'm guessing you mean



625 is 54



Divide both sides by 57x



To divide on the right, subtract exponents of 5



Take logs of both sides:



Use a rule of logarithms to move the exponents
in front of the logs:



To make things less messy, let A=log(2) and B=log(5)
















Edwin
RELATED QUESTIONS

Solve the following exponential equation. e^x+e^-x=5 The​ solution(s) is/are... (answered by Alan3354)
What is x in the following equation?... (answered by Theo)
Please solve the exponential equation:... (answered by Alan3354)
Solve the exponential equation... (answered by stanbon)
5.3 Solve the following exponential equation by expressing each side as a power of the (answered by ikleyn,MathTherapy)
Solve the equation. √5x+39-8=3x-15 The solution set is ​ ​​... (answered by ikleyn)
These 3 problems are from a worksheet, not a textbook, and I so desperately need them... (answered by scott8148)
Solve the following equation for x, 1/x-2 + 5/x+2 = 7x/x^2-4. The solution is... (answered by ewatrrr)
Answer the questions about the following function. F(x)=x+12/x-4 ​(a) Is (answered by Fombitz)