Express the equations in logarithmic form a 43 64 b103 000

Express the equations in logarithmic form.

(a) 4³ = 64

(b)10³ = 0.001

(c) e^x = 7

(d) e⁹ = y

Solution

a)4³=64

take logarithm on both sides

log(4³)=log(64)

3 log(4)=log(64)

b)10^-3=0.001

take logarithm on both sides

log(10^-3)=log(0.001)

-3log(10)=log(0.001)

log(0.001)=-3

c)e^x=7

take natural logarithm on both sides

ln(e^x)=ln(7)

xln(e)=ln(7)

x=ln(7)

d)e⁹=y

take natural logarithm on both sides

ln(e⁹⁾=ln(y)

ln(y)=9ln(e)

ln(y)=9