SOLUTION: Solve for X. 8raised to the power of x+4 is equal to 16raised to the power of 4x-3. 8^x+4=16^4x-3

Algebra ->  Exponents -> SOLUTION: Solve for X. 8raised to the power of x+4 is equal to 16raised to the power of 4x-3. 8^x+4=16^4x-3      Log On


   

Question 1148413: Solve for X. 8raised to the power of x+4 is equal to 16raised to the power of 4x-3.
8^x+4=16^4x-3
Found 3 solutions by josgarithmetic, ikleyn, josmiceli:
Answer by josgarithmetic(39621) About Me  (Show Source):
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

Left  side is  8^(x+4) = (2^3)^(x+4) = 2^(3*(x+4)).


Right side is  16^(4x-3) = (2^4)^(4x-3) = 2^(4*(4x-3)).


Thus  2^(3*(x+4)) = 2^(4*(4x-3)).


Since the numbers are equal and the bases are the same,  indexes are equal:


    3*(x+4) = 4*(4x-3)


    3x + 12 = 16x - 12

    12 + 12 = 16x - 3x

    24      = 13x


ANSWER.  x = 24%2F13.

Solved, explained and completed.



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+8%5E%28+x+%2B+4+%29+=+16%5E%28+4x+-+3+%29+
+%28+2%5E3+%29%5E%28+x+%2B+4+%29+=+%28+2%5E4+%29%5E%28+4x+-+3+%29+
Use the rule:
+%28+a%5Eb+%29%5Ec+=+a%5E%28+b%2Ac+%29+
---------------------------------
+2%5E%28+3%2A%28+x+%2B+4+%29+%29+=+2%5E%28+4%2A%28+4x+-+3+%29+%29+
+3%2A%28+x+%2B+4+%29+=+4%2A%28+4x+-+3+%29+
+3x+%2B+12+=+16x+-+12+
+13x+=+24+
+x+=+24%2F13+
------------------------
check:
+8%5E%28+x+%2B+4+%29+=+16%5E%28+4x+-+3+%29+
+8%5E%28+24%2F13+%2B+52%2F13+%29+=+16%5E%28+4%2A%2824%2F13%29+-+39%2F13+%29+
+8%5E%28+76%2F13+%29+=+16%5E%28+96%2F13+-+39%2F13+%29+
+8%5E%28+76%2F13+%29+=+16%5E%28+57%2F13+%29+%29+
+2%5E%28+3%2A%2876%2F13%29%29+=+2%5E%28+4%2A%2857%2F13%29%29+
+2%5E%28+228%2F13+%29+=+2%5E%28+228%2F13+%29+
OK
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