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Help with exponential equations (algebra 2)

Both need to be rounded to the nearest ten thousandths.

1. 4x=243

2. 14^x+1=36?I have do this problem too many times but only answers I have gotten is 1.347 or 0.358

 

Comments

Jackie, first equation is not exponential. Make sure you copied it correctly.

3 . 9 6 2 4 1 ˜ 3.9624 (round down)
             ?
       ten thousandth
next digit is 1 and is less than 5
0 . 3 5 7 8 7 ˜ 0.3579 (round up)
             ?
        ten thousandth
next digit is 7 and is greater than or equal 5

3.96241 ˜ 3.9624 (round down)
3 - ones
.
9 - tenth
6 - hundredth
2 - thousandth
4 - ten thousandths
1 - less than 5

0.35787 ˜ 0.3579 (round up)
0
.
3 - tenth
5 - hundredth
7 - thousandth
8 - ten thousandths
7 - greater than 5

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2 Answers

1.    4^x = 243  apply log on both side 

log 4^x = log 243    Now use power rule and bring x in the front

x log 4 = log 243     solve for x

x =  log   243 / log 4  Now enter it in the calculator

x = 3.96241  ANSWER

2.    14^(X+1) = 36  apply logs on both side

log 14^(X+1) = log 36  now use power rule and bring the x+1 in the front

(x+1) log 14 = log 36     divide over log14

x+1 = log 36/ log 14    now subtract 1 on the other side

x = (log 36/log 14) -1  use calculator

x = .35787  ANSWER

 

 

 

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