SOLUTION: please help me find the valiue of the letter X: {{{ -7/5^x+7/2=3/5^x+9/10 }}}

Algebra ->  Equations -> SOLUTION: please help me find the valiue of the letter X: {{{ -7/5^x+7/2=3/5^x+9/10 }}}      Log On


   

Question 204564: please help me find the valiue of the letter X:
+-7%2F5%5Ex%2B7%2F2=3%2F5%5Ex%2B9%2F10+
Found 2 solutions by nerdybill, MathTherapy:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
+-7%2F5%5Ex%2B7%2F2=3%2F5%5Ex%2B9%2F10+
Begin by multiplying both sides by 5^x
+-7%2B%287%2F2%295%5Ex=3%2B%289%2F10%295%5Ex+
Next, multiply both sides by 10:
+-70%2B%2835%295%5Ex=30%2B%2827%295%5Ex+
+-70%2B%288%295%5Ex=30+
+%288%295%5Ex=100+
+5%5Ex=100%2F8+
Take log base 5 of both sides:
+x=log%285%2C100%2F8%29+
+x=log%285%2C12.5%29+
+x=log%2812.5%29%2Flog%285%29+
+x=1.569+

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

-7%2F5%5Ex%2B7%2F2=3%2F5%5Ex%2B9%2F10
-7%2810%29+%2B+35%2A5%5Ex+=+30+%2B+9%2A5%5Ex ------> Multiply by LCD, 10%2A5%5Ex
-70+%2B+26%2A5%5Ex+=+30
26%2A5%5Ex+=+100
5%5Ex+=+100%2F26
5%5Ex+=+3.846153846
x+=+log%285%2C3.846153846%29
highlight_green%28x++=++0.836983917%29