Solve this unknown exponents by the law of logarithm equation 27^3t_1=9.

Answer 1

To solve for the unknown exponent, we can rewrite the equation using the property that 27 can be expressed as 3^3:

3^(3*3t_1) = 9

Now we can simplify the equation by multiplying the exponents:

3^(9t_1) = 9

Next, we can rewrite 9 as 3^2:

3^(9t_1) = 3^2

Now we can equate the exponents:

9t_1 = 2

Finally, we can solve for t_1 by dividing both sides by 9:

t_1 = 2/9

Therefore, the solution for the unknown exponent t_1 is 2/9.