How do you solve 6^x=216? Precalculus Properties of Logarithmic Functions Natural Logs 1 Answer KillerBunny Oct 13, 2016 x=3 Explanation: You can decompose 216 to see its prime factors: 216 \div 2 = 108 108 \div 2 = 54 54 \div 2 = 27 27 \div 3 = 9 9 \div 3 = 3 3 \div 3 = 1 Thus, 2016 = 2^3 * 3^3 But this means that 2016 = (2*3)^3=6^3, and thus x=3 Answer link Related questions What is the natural log of e? What is the natural log of 2? How do I do natural logs on a TI-83? How do I find the natural log of a fraction? What is the natural log of 1? What is the natural log of infinity? Can I find the natural log of a negative number? How do I find a natural log without a calculator? How do I find the natural log of a given number by using a calculator? How do I do natural logs on a TI-84? See all questions in Natural Logs Impact of this question 3873 views around the world You can reuse this answer Creative Commons License