Final answer:
To rewrite 6 log5 x^3 without exponents, multiply the inside exponent by the coefficient to get log5 (x^3)^6, which simplifies to log5 x^18. There's no further algebraic simplification to remove the exponent while retaining standard notation.
Step-by-step explanation:
To rewrite 6 log5 x^3 without using exponents, we can apply the laws of logarithms and the properties of exponents. The given expression can be simplified by multiplying the exponent inside the logarithm by the coefficient outside to obtain:
log5 (x^3)^6
According to the properties of exponents, when raising a power to a power, we multiply the exponents:
x^3 raised to the power of 6 becomes x^(3*6) or x^18.
Therefore, the expression can be rewritten as:
log5 x^18
Now, the exponent has been simplified to a single degree. However, if we need to express this completely without exponents, we understand that there are no operations or simplifications that can convert x^18 to a base number without an exponent while remaining within the realms of typical algebraic notation. In contexts where exponents are not acceptable, this would be handled differently, perhaps using repeated multiplication or another notation system.