To solve for x, we need to simplify the equation first.
23^(x+1) - 92^(x+1) = 92^x - 23^x
Expanding the exponents:
233^x - 922^x = 92^x - 23^x
63^x - 182^x = 92^x - 23^x
Rearranging terms:
63^x + 23^x = 92^x + 182^x
Combining like terms:
83^x = 272^x
Dividing both sides by 3^x and 2^x:
8 = 27(2/3)^x
To solve for x, take the natural logarithm of both sides:
ln(8) = ln(27(2/3)^x)
ln(8) = ln(27) + x*ln(2/3)
ln(8) = ln(27) + x(ln(2) - ln(3))
ln(8) = ln(27) + x(ln(2/3))
ln(8) - ln(27) = x(ln(2/3))
ln(8/27) = x(ln(2/3))
x = ln(8/27) / ln(2/3)
x ≈ -0.9543
Therefore, x is approximately -0.9543.
To solve for x, we need to simplify the equation first.
23^(x+1) - 92^(x+1) = 92^x - 23^x
Expanding the exponents:
233^x - 922^x = 92^x - 23^x
63^x - 182^x = 92^x - 23^x
Rearranging terms:
63^x + 23^x = 92^x + 182^x
Combining like terms:
83^x = 272^x
Dividing both sides by 3^x and 2^x:
8 = 27(2/3)^x
To solve for x, take the natural logarithm of both sides:
ln(8) = ln(27(2/3)^x)
ln(8) = ln(27) + x*ln(2/3)
ln(8) = ln(27) + x(ln(2) - ln(3))
ln(8) = ln(27) + x(ln(2/3))
ln(8) - ln(27) = x(ln(2/3))
ln(8/27) = x(ln(2/3))
x = ln(8/27) / ln(2/3)
x ≈ -0.9543
Therefore, x is approximately -0.9543.