SOLUTION: I need help with these two problems please! Solve for x without tables: 1) x = log(base 5) 1 x= ____ 2) x = log(base e)sqrt of e x= _____ ~Sarah

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I need help with these two problems please! Solve for x without tables: 1) x = log(base 5) 1 x= ____ 2) x = log(base e)sqrt of e x= _____ ~Sarah      Log On


   

Question 202471: I need help with these two problems please!

Solve for x without tables:

1) x = log(base 5) 1
x= ____

2) x = log(base e)sqrt of e
x= _____

~Sarah
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

x=log%285%2C%281%29%29 Start with the given equation.


x=log%285%2C%285%5E0%29%29 Rewrite 1 as 5%5E0


Note: x%5E0=1 for all any x where x%3C%3E0


x=0%2Alog%285%2C%285%29%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x=0 Multiply


So the solution is x=0






# 2


x=log%28e%2C%28sqrt%28e%29%29%29 Start with the given equation.


x=log%28e%2C%28e%5E%281%2F2%29%29%29 Convert to exponential notation.


x=%281%2F2%29log%28e%2C%28e%29%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


x=%281%2F2%29%281%29 Evaluate the log base "e" of "e" to get 1


x=1%2F2 Multiply


So the solution is x=1%2F2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Comment: log mean "exponent" or "power".
-----------------
1) x = log(base 5) 1
Comment: Your problem says "x is the exponent of 5 that gives you 1"
5^x = 1
x= 0____
===============================
2) x = log(base e)sqrt of e
Comment: Your problem says "x is the exponent of e that gives you (e)^(1/2).
e^x = e^(1/2)
x= (1/2)_____

============================
Cheers,
Stan H.