Examples of Math Problems: Solve the following exponential equation 3^(2x-1) = 2^(x+2)

Friday, May 3, 2013

Solve the following exponential equation 3^(2x-1) = 2^(x+2)

3%5E%282x-1%29+=+2%5E%28x%2B2%29

Expanding exponents...
3%5E%282x%29%2A3%5E%28-1%29+=+2%5Ex%2A2%5E2

3%5E%282x%29%2A3%5E%28-1%29+=+2%5Ex%2A2%5E2

simplifying...
3%5E%282x%29%2F3+=+2%5Ex%2A4

3%5E%282x%29%2F3+=+2%5Ex%2A4

%283%5E2%29%5Ex%2F3=4%2A2%5Ex

Next we isolate x...
9%5Ex%2F3=4%2A2%5Ex

9%5Ex%2F3=4%2A2%5Ex

9%5Ex%2F2%5Ex=4%2A3

Key step: we can combine the bases under the exponent since the exponent for both of them is the same...
%289%2F2%29%5Ex=12

%289%2F2%29%5Ex=12

log%28%289%2F2%29%5Ex%29=log12

x%2Alog%289%2F2%29=log12%29

x=log12%2Flog%289%2F2%29

which can be rewritten as...
log12%2F%28log9-log2%29

log12%2F%28log9-log2%29

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