Expanding/Condensing Logarithms
Condense the Logarithms:
log_3(2x)-log_3(5y)
log_3((2x)/(5y))
Solve for x:
log_x(216)=3
x=6
Evaluate:
ln(-2)
undefined
Determine whether the following sequence is geometric:
2, -6, 18, -54, ...
Yes, the sequence is geometric.
Condense the Logarithms:
2ln(3)+4ln(y)-2ln(x)
ln((9y^4)/x^2)
Solve for x:
3^(x+1)=216
x=3.89
Evaluate:
log_3(49)
3.54
Determine the common ratio of the geometric sequence:
-2, 4/3, -8/9, 16/27, ...
r=-2/3
Completely Expand the Logarithm:
log((2x)/y)
log(2)+log(x)-log(y)
Solve for x:
log_5(x+6)=log_5(3x)
x=3
Convert to Logarithmic Form:
2^x=8
log_2(8)=x
Write the explicit definition for the following sequence:
625, 125, 25, 5, 1, ...
a_n=625(0.2)^(n-1)
Condense the Logarithms:
3log(x)-4log(2)-5log(z)+3log(3)
log((27x^3)/(16z^5))
Solve for x:
3log(4)-log(x)=log(2)
x=32
Convert to Exponential Form:
-2=log_4(1/16)
(4)^(-2)=1/16
Find the sum of the series:
8+16+32+...+2,048
4,088
Completely Expand the Logarithm:
log_7((3x^6y^7)/(7z^5))
log_7(3)+6log_7(x)+7log_7(y)-1-5log_7(z)
Solve for x:
2log(x)=log(3x+4)
x=4
-1 is an extraneous solution
Find the inverse of the function:
f(x)=2^(x+4)
f^-1(x)=log_2(x)-4
The sum of a series is 31.75. The first term is 16, and its common ratio is 0.5. How many terms are in the series?
7