log7(17)

Multiply 17 by 77.

log7(17⋅77)

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

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)