Rewrite the statement log⁡(P)=5t using exponents instead of logs.?

Question

This is confusing to me as Logs usually have a number with it: ( ex. log_b(x) )

Please explain this as soon as you can. Is this the same as log_1(p) ??? I don't understand

Answer 1

// If no base is specified, the default base is 10

log P = 5t    ⇔    10⁵ᵗ = P  .............ANS

Answer 2

If a log doesn't have a base shown, you can usually assume it's a base 10 log.

so:

log(P) = 5t

is the same as:

P = 10^(5t)

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If the log is shown as "ln" then it's a base "e" log:

ln(P) = 5t

P = e^(5t)