We can start by simplifying the left-hand side of the equation:
1^x + 2^x = 1 + 2^x
Now we can substitute this
contexto expression back into the original equation to get:
1 + 2^x = 4^x
We can rewrite 4 as 2^2, and then apply the exponent rules for products to get:
1 + 2^x = (2^2)^x = 2^(2x)
Now we have an equation with only one base, so we can use logarithms to solve for x:
log₂(1 + 2^x) = log₂(2^(2x))
log₂(1 + 2^x) = 2x
Now we can use the change-of-base formula to rewrite the left-hand side in terms of natural logarithms:
ln(1 + 2^x) = 2x / ln(2)
Is that true?
