How can you solve Log(base x)6^x=(x/3)?

Question

How can you solve Log(base x)6^x=(x/3)?

Answer 1

I will write base x as bx

log(bx) 6^x = x/3

By power rule we can write as

          x log(bx) 6 = x/3

          log(bx) 6 = 1/3.......................x gets cancelled on both sides

Bringing to exponential terms,

    x^1/3= 6

Cubing on both sides

    x = 6³

    x = 216

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