Question

3 ^ (2x) - 2 ^ (x + 1) * 3 ^ x - 3 * 2 ^ (2x) = 0 .

Answer 1

log₁.₅3 or 2.70951

Explanation:

• 3^(2x) - 2^(x + 1) * 3^x - 3*2^(2x) = 0
• 3^(2x)- 2*2^x*3^x + 2^(2x)- 4*2^(2x)=0
• (3^x-2^x)^2 - (2*2^x)^2=0
• (3^x-2^x+2*2^x)(3^x - 2^x - 2*2^x)=0
• (3^x+2^x)(3^x- 3*2^x)=0
• 3^x+2^x>0 for any value of x
• 3^x- 3*2^x=0
• 3^x= 3*2^x
• 3^x/2^x=3
• 1.5^x=3
• x= log₁.₅ 3 = 2.70951