Properties of Exponents
Simplify the expression; no negative exponents.
-13y^5(9x^3y^2)
-117x^3y^7
Condense the logarithm.
8logk+3loga
logk^8a^3
Convert the exponent to logarithmic form.
2^5=32
log_2(32)=5
Evaluate the log.
log_9(81)
2
Solve for x.
9^(3x-7)=9^(5-x)
x = 3
Solve the exponential. Round your solution to the nearest ten-thousandth.
3^x=18
x=2.6309
Simplify the expression; no negative exponents.
(6z^6)/(-2z^-5)^2
(3z^16)/2
Expand the logarithm.
log((x^3z^4)/y)
3logx+4logz-logy
Convert the logarithm to exponential form.
log_2(8)=3
2^3=8
Evaluate the log.
log_8(8)
1
Solve for x.
1/5=5^(2x+3)
x = -2
Solve the exponential. Round your solution to the nearest ten-thousandth.
5-3^(x+2) = 9
No solution!
Simplify the expression; no negative exponents.
((-3a^-1)^3)/(-6a^10)
9/(2a^13)
Expand the logarithm.
log(y^2/(x^4z))
2logy-4logx-logz
Write the logarithm in exponential form.
log_2(1/64)=-6
2^-6 = (1/64)
Evaluate the log.
log_12(1)
0
Solve for x.
2^(3x-1)*2^(5x-7)=16
x = 3/2
Solve the exponential. Round your solution to the nearest ten-thousandth.
15^(3x-5)=87
x=2.2164
Simplify the expression; no negative exponents.
(-4(n^-2)^2)/(-5n^-5)
(4n)/5
Condense the numeric logarithm.
3log_b5
log_b(125)
Write the exponent as a logarithm.
7^(1/2) = sqrt(7)
log_7(sqrt7)=1/2
Evaluate the log.
log (1/10)
-1
Solve for x.
36^(x-3)*216^x=216^(2x+1)
x=-9
Solve the exponential. Round your solution to the nearest ten-thousandth.
9*12^(x+4)-8=127
x=-2.9102
Simplify the expression; no negative exponents.
((3t^-4n^-5)^-3)/(4n^3)
(t^12n^12)/108
Condense the numeric logarithm.
log_b8-3log_b2
log_b(1)
Convert the logarithm to exponential form.
log_7(sqrt(343))=3/2
7^(3/2)=sqrt(343)
Evaluate the log.
log_5sqrt(5)
1/2
Solve for x.
(1/9)^x*(1/3)^x=3^(16-x)
x=-8
Solve the exponential. Round your solution to the nearest ten-thousandth.
8*11^(3x-9)+10=194
x=3.4359