Converting exponentials into logarithms
We know how to solve and manipulate logarithms (see laws of logarithms), but what if we have an exponential expression that we want to convert into a logarithmic one?
We can just use the definition of logarithms to rewrite the exponential
expression
Convert 2^3=8 into a logarithmic expression
\log_2(8)
Convert 5^x=25 into a logarithmic expression
x=\log_5(25) x=2
Solve for x : 3^x=27
x=\log_3(27) x=3
Solve for x : 10^{x-1}=1000
x-1=\log_{10}(1000) x-1=3 x=4
Find the exact value of x : e^{2x}=7
2x=\ln(7) x=\frac{\ln(7)}{2}
Find the exact value of x : 4^{x+1}=16
x+1=\log_4(16) x+1=2 x=1
Solve for x : (2^x)^3=64
3x=\log_2(64) 3x=6 x=2
Solve for x : (5^{2x-1})^2=125
5^{2(2x-1)}=125 5^{4x-2}=125 4x-2=\log_5(125) 4x-2=3 4x=5 x=\frac{5}{4}