SOLUTION: How do I solve logarithms with square roots? For example the value of logarithms with base √2 and number 8√2 equals to 7. But how to you get the final answer without

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I solve logarithms with square roots? For example the value of logarithms with base √2 and number 8√2 equals to 7. But how to you get the final answer without       Log On


   



Question 998758: How do I solve logarithms with square roots?
For example the value of logarithms with base √2 and number 8√2 equals to 7. But how to you get the final answer without a calculator?

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the value of logarithms with base √2 and number 8√2 equals to 7
-----
log(sqrt(2))of 8sqrt(2) = 7
----
Write that as an exponential equation::
base = sqrt(2)
log = exponent = 7
result = 8sqrt(2)
---------
Exp. Eq:: (sqrt(2))^7 = 8sqrt(2)
------
(2^(1/2))^7 = 2^3*2^(1/2)
-----------
2^(7/2) = 2^(3 1/2)
-----------
2^(7/2) = 2^(7/2)
-----------
Cheers,
Stan H.
----------------

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

log%28sqrt%282%29%2C8sqrt%282%29%29=+7......change the base to base 10
log%288sqrt%282%29%29%2Flog%28sqrt%282%29%29=+7
log%288sqrt%282%29%29=+7log%28sqrt%282%29%29
log%288sqrt%282%29%29=+log%28%28sqrt%282%29%29%5E7%29...if log same, than
8sqrt%282%29=+%28sqrt%282%29%29%5E7

8sqrt%282%29=+2%2A2%2A2%2Asqrt%282%29
8sqrt%282%29=+8sqrt%282%29...since left and right side of equation sign are same, the statement log%28sqrt%282%29%2C8sqrt%282%29%29=+7 is true