3=81⋅r10-1

Rewrite the equation as 81⋅r10-1=3.

81⋅r10-1=3

Subtract 1 from 10.

81⋅r9=3

Divide each term in 81⋅r9=3 by 81.

81⋅r981=381

Cancel the common factor of 81.

Cancel the common factor.

81⋅r981=381

Divide r9 by 1.

r9=381

r9=381

Cancel the common factor of 3 and 81.

Factor 3 out of 3.

r9=3(1)81

Cancel the common factors.

Factor 3 out of 81.

r9=3⋅13⋅27

Cancel the common factor.

r9=3⋅13⋅27

Rewrite the expression.

r9=127

r9=127

r9=127

r9=127

Take the 9th root of both sides of the equation to eliminate the exponent on the left side.

r=1279

Rewrite 1 as 13.

r=13279

Rewrite 27 as 33.

r=13339

Rewrite 1333 as (13)3.

r=(13)39

Rewrite (13)39 as (13)333.

r=(13)333

Pull terms out from under the radical, assuming real numbers.

r=133

Rewrite 133 as 1333.

r=1333

Any root of 1 is 1.

r=133

Multiply 133 by 332332.

r=133⋅332332

Combine and simplify the denominator.

Multiply 133 and 332332.

r=33233332

Raise 33 to the power of 1.

r=332331332

Use the power rule aman=am+n to combine exponents.

r=332331+2

Add 1 and 2.

r=332333

Rewrite 333 as 3.

Use axn=axn to rewrite 33 as 313.

r=332(313)3

Apply the power rule and multiply exponents, (am)n=amn.

r=332313⋅3

Combine 13 and 3.

r=332333

Cancel the common factor of 3.

Cancel the common factor.

r=332333

Divide 1 by 1.

r=33231

r=33231

Evaluate the exponent.

r=3323

r=3323

r=3323

Simplify the numerator.

Rewrite 332 as (32)13.

r=3233

Raise 3 to the power of 2.

r=933

r=933

r=933

The result can be shown in multiple forms.

Exact Form:

r=933

Decimal Form:

r=0.69336127…

Solve for r 3=81*r^(10-1)