PLS HELP OFFERING 15 POINTS
Solve the equation for x.

2^(x+1) = 3^(-x+1)

x=0.2262943855

Step-by-step explanation:

Properties of exponents: 2^(x+1)=(2^x)(2^1)=2(2^x)

Properties of exponents: 3^(-x+1)=(3^-x)*(3^1)=(1/(3^x))*3=3/(3^x)

So:

2(2^x)=3/(3^x)

2(2^x)(3^x)=3

2(6^x)=3 (Remember that different bases w/ same exponents have their bases multiplied)

6^x=1.5

Take the base 6 logarithm: log6(6^x)=log6(1.5)

x=0.2262943855

answer: approximately 206 bones

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