Hello,(adsbygoogle = window.adsbygoogle || []).push({});

The following problem is bothering me quite a bit. It is...

Solve.

3 x 2^x = 12

The Unit this question is in is about solving exponential equations through expressing each side as a power of the same base, by taking a base (x) logarithm of each side or taking a base 10 logarithm of each side.

The answer is supposed to be 2. Here are my calculations.

3 x 2^x = 12

log 3 + xlog 2 = log 12

x(log 3 - log 2) = log 12

xlog 3/2 = log 12

x = log 12 / log 2/3

Now this is incorrect for probably more then one reason. I've had success doing the questions of the form... 3^3x-1 = 9^2x. But when they introduced multiplication on the left side of the eq I got lost. Also I noticed that 3 or 2 cannot have a whole number exponent to make 12. Confusion is upon me. Thanks for the help in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solving Exponential Equations Using Logarithms

**Physics Forums | Science Articles, Homework Help, Discussion**