find the value of log 8 to the base root 2
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5
Rewrite as an equation.
log8(2)=x
Rewrite log8(2)=x
in exponential form using the definition of a logarithm. If x and b are positive real numbers and b does not equal 1, then logb(x)=y is equivalent to by=x
.
8x=2
Create expressions in the equation that all have equal bases.
(23)x=21
Rewrite (23)x
as 23x
.
23x=21
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
3x=1
Solve for x
.
x=13
The variable x
is equal to 13
.
13
The result can be shown in multiple forms.
Exact Form:
13
Decimal Form:
0.¯3
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