SOLUTION: Use like bases to solve the exponential equation for x. 256 · 4^(9x + 3) = 64

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Question 1059802: Use like bases to solve the exponential equation for x.
256 · 4^(9x + 3) = 64
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Express the whole thing using base-two.

64=8%5E2=%282%5E3%29%5E2=2%5E6

256=2%5E8


----
4%5E%289x%2B3%29=64%2F256
%282%5E2%29%5E%289x%2B3%29=%282%5E6%29%2F%282%5E8%29
2%5E%282%289x%2B3%29%29=1%2F2%5E2
2%5E%2818x%2B6%29=2%5E%28-2%29
You should understand, left and right members each are the base 2, raised to different expressioned exponents. The exponents must be equal. You can try taking logarithms-base two of both members, but you should understand through corresponding parts without the taking of logs....


18x%2B6=-2
18x=-8
highlight%28x=-4%2F9%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Use like bases to solve the exponential equation for x.
256 · 4^(9x + 3) = 64 
256+%2A+4%5E%289x+%2B+3%29+=+64

4%5E4+%2A+4%5E%289x+%2B+3%29+=+4%5E3 ------ Converting 256 and 64 to base 4

4%5E%284+%2B+9x+%2B+3%29+=+4%5E3 ------ Applying a%5Eb+%2A+a%5Ec+=+a%5E%28b+%2B+c%29

4 + 9x + 3 = 3 ------- Bases are equal and so are the exponents

7 + 9x = 3

9x = - 4

highlight_green%28x+=+-+4%2F9%29