what is 3^x = 81

Question

solve without using log

Answer 1

3^x = 81 = 9^2 = (3^2)^2 = 3^4

3^x = 3^4

x = 4

everything is identical on both sides of the equation, except x and 4, so set them equal

3^4 = 3x3x3x3 =9x3x3 = 27x3 = 81

log(3^4) = log(81)

log81 = 4log3

1.9085 =4(0.4771)= 1.9085

log(3^x) = log81

xlog3 = log81

x = log81/log3=1.9085/0.4771=4

You could have the most complicated, convoluted incomprehensible mess on boths sides of an equation in the identical manner, except for one tiny detail,

notice x in the midst of it all one one side and 4 in the same position in the midst of it all on the other side and set them equal to get x=4

[(yx+b!/28pi)/z^2e]^yz/32= [(4y+b!28pi)/z^2e]^yz/32

x=4

also

3^x = 81 rewritten in log form is log₃81 = x

x = log₃81 = log81/log3 = about 1.9085/0.4771 = 4.0000