SOLUTION: Find all real solutions to the equations. If you eliminate a solution, show or explain why.? 4 log(base 5) (8-x) = 7 12(4^(3x)) = 120 Thank you

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find all real solutions to the equations. If you eliminate a solution, show or explain why.? 4 log(base 5) (8-x) = 7 12(4^(3x)) = 120 Thank you      Log On


   

Question 916894: Find all real solutions to the equations. If you eliminate a solution, show or explain why.?
4 log(base 5) (8-x) = 7

12(4^(3x)) = 120

Thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4%2Alog%285%2C%288-x%29%29=+7+
+log%285%2C%288-x%29+%5E4%29=+7+ ...in base 10 we have
+log%28%288-x%29+%5E4%29%2Flog%285%29=+7+
+log%28%288-x%29+%5E4%29=+7log%285%29+
+log%28%288-x%29+%5E4%29=+log%285%5E7%29+ .....if log same, then
+%288-x%29+%5E4=+5%5E7+
+%288-x%29+=+root%284%2C5%5E7%29+
+8-x+=+5%2A+root%284%2C5%5E3%29
+x=8-+5%2A+root%284%2C5%5E3%29+ ...exact value..............root%284%2C5%5E3%29+=3.3437 (approximately)
+x=8-+5%2A+3.3437
+x=8-+16.7185
+x=-8.7185



12%284%5E%283x%29%29+=+120+
4%5E%283x%29+=+120%2F12+
4%5E%283x%29+=+10+
log%284%5E%283x%29+%29=log%28+10+%29
3x%2Alog%284+%29=log%28+2%2A5+%29
3x%2Alog%282%5E2+%29=log%28+2%29-log%285+%29
2%2A3x%2Alog%282+%29=log%28+2%29-log%285+%29
6x%2Alog%282+%29=log%28+2%29-log%285+%29
x=%28log%28+2%29-log%285+%29%29%2F6log%282%29