# Evaluate log base 7 of 1/( square root of 7)

log7(17)
Multiply 17 by 77.
log7(17⋅77)
Combine and simplify the denominator.
Multiply 17 and 77.
log7(777)
Raise 7 to the power of 1.
log7(7717)
Raise 7 to the power of 1.
log7(77171)
Use the power rule aman=am+n to combine exponents.
log7(771+1)
Add 1 and 1.
log7(772)
Rewrite 72 as 7.
Rewrite 7 as 712.
log7(7(712)2)
Apply the power rule and multiply exponents, (am)n=amn.
log7(7712⋅2)
Combine 12 and 2.
log7(7722)
Cancel the common factor of 2.
Cancel the common factor.
log7(7722)
Divide 1 by 1.
log7(771)
log7(771)
Evaluate the exponent.
log7(77)
log7(77)
log7(77)
Rewrite 77 as 7⋅7-1.
log7(7⋅7-1)
Rewrite log7(7⋅7-1) as log7(7)+log7(7-1).
log7(7)+log7(7-1)
Use logarithm rules to move -1 out of the exponent.
log7(7)-log7(7)
Logarithm base 7 of 7 is 1.
log7(7)-1⋅1
Multiply -1 by 1.
log7(7)-1
Rewrite log7(7) using the change of base formula.
The change of base rule can be used if a and b are greater than 0 and not equal to 1, and x is greater than 0.
loga(x)=logb(x)logb(a)-1
Substitute in values for the variables in the change of base formula, using b=10.
log(7)log(7)-1
log(7)log(7)-1
The result can be shown in multiple forms.
Exact Form:
log(7)log(7)-1
Decimal Form:
-0.5
Evaluate log base 7 of 1/( square root of 7)

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