SOLUTION: I have solved these equations but the directions require me to show work or provide an explanation and I don't know how.Here are the questions: Write each of the following in expo

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I have solved these equations but the directions require me to show work or provide an explanation and I don't know how.Here are the questions: Write each of the following in expo      Log On


   



Question 1007501: I have solved these equations but the directions require me to show work or provide an explanation and I don't know how.Here are the questions:
Write each of the following in exponential form:
1) log3 x = 9
3^9= x

2) log2 8 = x
8= 2^x
3) ln x = 2
e^2 = x
4) log x = 5
10^5= x

Found 2 solutions by rothauserc, MathLover1:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We use the definition of logarithm
y = log base b of x means that x = b^y
**********************************************************************
1) log base 3 of x = 9, then 3^9 = x
2) log base 2 of 8 = x, then 8 = 2^x
3) ln of x = 2, then e^2 = x
4) log x = 5, then 10^5 = x

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1)
log%283%2C+x%29+=+9
3%5E9=+x......here you have used the relationship:log%28b%2Cy%29+=+x is equivalent to (means the exact same thing as) y+=+b%5Ex
x=3%2A3%2A3%2A3%2A3%2A3%2A3%2A3%2A3
x=+19683
2)
+log%282%2C+8%29+=+x.....same explanation here too
8=+2%5Ex....now write 8 as 2%5E3 to have same base
2%5E3=+2%5Ex use the rule if bases same, exponents are same too
so, x=3

3)
ln+%28x%29+=+2
e%5E2+=+x since e=2.7182818284590452353602874713526624977572470936999596+, approximately e=2.71828
x=%282.71828%29%5E2
x=7.3891
4)
log+%28x%29+=+5...same explanation here too as in 1 and 2
10%5E5=+x
x=10%2A10%2A10%2A10%2A10
x=100000