Solve Exponential Equations
Solve
3^(3x-5)>81
x>3
Write the exponential equation of the function that passes through the points (0,1) and (-1,4).
y=1(1/4)^x
Write in logarithmic form
5^3=125
log_5 125=3
Simplify
log_7 49
2
Solve
log_3 81=x
x=4
Solve
7^(6x)=7^(2x-20)
x=-5
Write the exponential equation of the function that passes through the points (0,2) and (1,10).
y=2(5)^x
Write in logarithmic form
3^4=81
log_3 81=4
Combine
log_3 4+log_3 x
log_3(4x)
Solve
log_3 3^(4x+3)=11
x=2
Solve
9^(2x-1)=27^(x-4)
x=-10
Write the exponential equation of the function that passes through the points (0,3) and (-1,6)
y=3(1/2)^x
Write in logarithmic form
2^3=8
log_2 8=3
Combine
3log_2 x-2log_2 y
log_2(x^3/y^2)
Solve
4^(3x)=12
x=log12/(3log4)
Solve
3^(6x-5)<9^(4x-3)
x>1/2
Write the exponential equation of the function that passes through the points (0,4) and (1,12)
y=4(3)^x
Write in exponential form
log_3 243=5
3^5=243
Separate
log_5((x^2y)/z^3)
2log_5 x+log_5 y-3log_5z
Solve
lnx+ln3=4
(e^4)/3
Solve
2^(3x-1)>=(1/8)^x
x>=1/6
Write the exponential equation of the function that passes through the points (0,1) and (-1,3)
y=1(1/3)^x
Write in exponential form
log_4 64=3
4^3=64
Separate
log_7(a/(b^2c))
log_7a-2log_7b-log_7c
Solve
e^(2x)+1=55
x=ln54/2