SOLUTION: Please help me solve this equation: 3^0.16x=1.5 i've tried to take logs of both sides but it doesn't come out with the right answer. Thanks in advance!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me solve this equation: 3^0.16x=1.5 i've tried to take logs of both sides but it doesn't come out with the right answer. Thanks in advance!      Log On


   

Question 112248: Please help me solve this equation:
3^0.16x=1.5
i've tried to take logs of both sides but it doesn't come out with the right answer.
Thanks in advance!
Found 2 solutions by bucky, Edwin McCravy:
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given to solve:
.
3^0.16x=1.5
.
If this is exactly the way the problem was presented to you, then by the rules of algebra this
problem is to be interpreted as:
.
3%5E0.16x=1.5
.
and 3%5E0.16 is just a calculator problem. It equals 1.192173326 and substituting
this into the equation reduces it to ...
.
1.192173326%2Ax+=+1.5
.
Then just divide both sides of the equation by 1.192173326 and you get:
.
x+=+1.5%2F1.102173326+=+1.258206308
.
However, if you meant the equation to be:
.
3%5E%280.16%2Ax%29+=+1.5
.
Then it is a whole different problem. In this case, you could solve it by taking the log
(assume base 10) of both sides and you would have:
.
log%2810%2C3%5E%280.16%2Ax%29%29+=+log%2810%2C1.5%29
.
Bring the exponent out as a multiplier and you have:
.
0.16%2Ax%2Alog%2810%2C3%29+=+log%2810%2C+1.5%29
.
A calculator tells you that log%2810%2C3%29+=+0.477121254 and log%2810%2C1.5%29+=+0.176091259.
Substitute these values into the equation and you have:
.
0.16%2Ax%2A%280.477121254%29+=+0.176091259
.
On the left side the 0.16 times 0.477121254 gives 0.0763394 ... substitute this value for
that product and the equation becomes:
.
0.0763394%2Ax+=+0.176091259
.
Divide both sides by 0.0763394 and you get:
.
x+=+0.176091259%2F0.0763394+=+2.30668904
.
Hope this helps to lead you to the correct answer.
.

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this equation:
3^0.16x=1.5
i've tried to take logs of both sides but it doesn't come out with the right answer.
Thanks in advance! 

3%5E%280.16x%29 = 1.5

Take the log10 of both sides:

log%2810%2C3%5E%280.16x%29%29 = log%2810%2C1.5%29  

Move the exponent 0.16x out in front of the
log as a coefficient.

0.16x%2Alog%2810%2C3%29 = log%2810%2C1.5%29

Divide both sides by 0.16%2Alog%2810%2C3%29

%280.16x%2Alog%2810%2C3%29%29%2F%280.16%2Alog%2810%2C3%29%29 = %28log%2810%2C1.5%29%29%2F%280.16%2Alog%2810%2C3%29%29

x = %28log%2810%2C1.5%29%29%2F%280.16%2Alog%2810%2C3%29%29

x = 0.1760912%2F%280.16%2A0.4771212547%29

x = 2.30668904

------------------------------

You can also do it by taking the natural log
of both sides instead of the log10:

3%5E%280.16x%29 = 1.5

Take the ln of both sides:

ln%283%5E%280.16x%29%29 = ln%281.5%29  

Move the exponent 0.16x out in front of the
ln as a coefficient.

0.16x%2Aln%283%29 = ln%281.5%29

Divide both sides by 0.16%2Aln%283%29

%280.16x%2Aln%283%29%29%2F%280.16%2Aln%283%29%29 = %28ln%281.5%29%29%2F%280.16%2Aln%283%29%29

x = %28ln%281.5%29%29%2F%280.16%2Aln%283%29%29

x = 0.4054651081%2F%280.16%2A1.098612289%29

x = 2.30668904

Edwin