SOLUTION: Solve. Round to four decimal places
a) e^3x >_ 21
b) (1/5)^t-2 = 125
Algebra.Com
Question 354347: Solve. Round to four decimal places
a) e^3x >_ 21
b) (1/5)^t-2 = 125
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
a)
Find the natural log (because of the "e" and because we want a decimal):
Use a property of logarithms, , to move the exponent out in front:
By definition, ln(e) = 1 so this simplifies to:
Divide both sides by 3:
b)
The quick way to solve this comes from recognizing that both sides are powers of 5: and . Subsituting these in we get:
On the left side the rule is to multiply exponents:
Now the equation explicitly says each side is a power of 5. And if these two powers of 5 are equal, then the exponents must be equal!
Solving this:
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