SOLUTION: Find the missing x or b a. log(2)x=2 b. log(b)4=2/3

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the missing x or b a. log(2)x=2 b. log(b)4=2/3      Log On


   

Question 599344: Find the missing x or b
a. log(2)x=2
b. log(b)4=2/3
Found 2 solutions by ankor@dixie-net.com, Earlsdon:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the missing x or b
:
a. log(2)x=2
write the exponent equiv of logs
x = 2^2
x = 4
so we have
log2[4] = 2
:
b. log(b)4=2/3
write the exponent equiv of logs
b%5E%282%2F3%29 = 4
Cube both sides
b%5E2 = 4%5E3
b%5E2 = 64
b = sqrt%2864%29
b = 8
so we have
log8[4] = 2%2F3

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
Log%5B2%5D%28x%29+=+2 Rewrite in exponential form. If Log%5Bb%5D%28x%29+=+y, then b%5Ey+=+x so...
2%5E2+=+x
x+=+4
Solve for b:
Log%5Bb%5D%284%29+=+2%2F3 Rewrite in exponential form:
b%5E%282%2F3%29+=+4 Raise both sides to the 3%2F2 power.
%28b%5E%282%2F3%29%29%5E%283%2F2%29+=+4%5E%283%2F2%29 Simplify.
b+=+sqrt%284%5E3%29
b+=+sqrt%2864%29
b+=+8