how to solve 2(3^x)=12

Question

Cant remember the proper way to solve

 

2(3^x)=12  I get to 2(log3)=log12

Answer 1

Daniel, to solve this you need to be comfortable with the logarithmic functions.

 

first divide both sides by 2 to make it easy on yourself

2*3^x = 12

3^x=6

 

now take the log base 3 of both sides to bring the variable (x) out of the exponent

 

x = log₃(6)

 

now use the change base so you can use your calculator.

 

x = log₁₀(6) / log₁₀(3) 

 

from a calculator (or from log tables if you want)

 

x = .7782 / .4771  = 1.6309

 

check by substituting back into the original equation and you find that

 

2 * [3^(1.6309)] ~ 12

 

Hence, x = 1.6309

 

The rule to remember is when the variable you are solving for is in the exponent, you will often have to use the log function to bring it down (out of the exponent) in order to solve for it.

 

note : these two equations are equivalent     

 

y = log_b(x)     <==>    x = b^y

 

Answer 2

Divinding both sides by 2,

3^x = 6

Taking ln,

xln3 = ln6

Answer: x = ln6/ln3, or x = log[3] 6, where 3 is the base.

Answer 3

2(3^x) = 12

3^x = 6

x = log₃ 6

x = 1.6309297536 ≈ 1.63