How do I solve this equation for x without a logarithm?
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What appliesand with
We draw a 2^(x-1) each on both sides and receive
We always share with 2
x-6=0, so that 2 high exponent = 1.
32 + 2^(x-1) = 2^x,
with:
32 = 2^5 = 2^x – 2^(x-1) = 2*2^(x-1) – 1*2^(x-1) = 2^(x-1).
Because of the injectivity of the exponential function, the following applies:
5 = x – 1,
with
x = 6
By subtraction
Think about what is 2^x – 2^(x-1).
I find the solution elegant!