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Kael Sanchez
Mathematics
16 March, 01:33
Solve for x
27=9^-x+5
+2
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2
)
Mercedes Murray
16 March, 01:39
0
1. Use negative power rule: x^-a=1/x^a
27=1/9^x+5
2. Subtract 5 from both sides
27-5=1/9^x
3. Simplify 27-5 to 22
22=1/9^x
4. Multiply both sides by 9^x
22*9^x=1
5. Divide both sides by 22
9^x=1/22
6. Use definition of common logarithm: b^a=x if and only if log (x) = a
x=log9 (1/22)
7. Use change of base rule: logbx = (logan) / 8logab)
x = (log1/22) / (log9)
8. Use power rule: logbx^c=clogbx log1/22 - > log (22^-1) - > - log22
x = (-log22) / (log9)
9. Use power rule
Use power rule: logbx^c=clogbx, log9 - > log3^2 - > 2 log3
x = (-log22) / (2log3)
10. Your answer is, and my wish of you having a nice day : D
x = - (log22) / (2log3)
x = (approx.) - 1.41
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Max Morgan
16 March, 01:59
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27 = 9^-x + 5
Subtract 5 from both sides
22 = 9^-x
Log 22 = - x log 9
(Log22) / (log9) = - x
- (log22) / (log9) = x
-1.41 = x
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