Is 1+log x =logex?

Yes, 1 + log x = log ex, if the base of the logarithm is e. If the base of the logarithm is e then the logarithm is known as natural logarithm.

If the base of logarithm is e, then we can write

1 = log e

1 + log x = log e + log x

( According to logarithmic property,

log mn = log m + log n)

1 + log x = log e + log x

= log ex

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