Convert number from base-10 number system to any number system

I wrote a small method for convert number from base-10 number system to any number system (code is not perfect but that is not the point).
My question is if I get right single responsibility principle. Is 2nd approach better than 1st or 'charReplace' functionality is too small for creating own method ?

public static string convertNumber(BigInteger num, int baseNum)
    {
        string symbols = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
        if (baseNum = 10)
            {
                result = result.Insert(0, symbols[partResult - 10].ToString());
            }
            else
            {
                result = result.Insert(0, partResult.ToString());
            }
            num /= baseNum;
        } while (num != 0);

        return result;
    }

vs.

static readonly string Symbols = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";

    public static string convertNumber(BigInteger num, int baseNum)
    {
        if (baseNum < 2 || Symbols.Length + 10 < baseNum)
        {
            throw new Exception;
        }

        var result = "";
        do
        {
            var partResult = (int)(num % baseNum);
            result = result.Insert(0, charReplace(partResult));
            num /= baseNum;
        } while (num != 0);

        return result;
    }

    private static string charReplace(int number){
        if (number < 10){
            return number.ToString();
        }

        return Symbols[number - 10].ToString();
    }

I believe the 1st approach is good enough since it personally more readable.

Little suggestions

• I'd prefer to store the whole alphabet in the symbols string, instead of only letters. This could simplify the logic.

• You can calculate the resulting length of the output string and avoid string insertions.

Summarizing:

public static string ConvertNumber(BigInteger num, int baseNum)
{
    const string symbols = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
    if (baseNum < 2 || symbols.Length < baseNum)
    {
        throw new ArgumentOutOfRangeException(nameof(baseNum));
    }

    if (num < 0)
    {
        throw new ArgumentOutOfRangeException(nameof(num));
    }

    var resultLength = 1 + Math.Max((int)BigInteger.Log(num, baseNum), 0);
    var result = new char[resultLength];
    int index = resultLength - 1;
    do
    {
        result[index--] = symbols[(int)(num % baseNum)];
        num /= baseNum;
    } while (num != 0);

    return new string(result);
}

PS. It's recommended to name all classes and all methods in UpperCamelCase regardless of their publicity.

StackExchange Code Review Q#157512, answer score: 2