What is the answer to 5+ln(x-1)=3 ?

The answer to 5+ln(x-1)=3 is x= 1/(e^2)+1

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5+ln(x-1)=3

5 + ln (x - 1) = 3

x = \frac{1}{e ^{2}} + 1

Decimal Notation

x = 1.13533 \dots

Solution steps

5 + ln (x - 1) = 3

Move

5

to the right side

ln (x - 1) = - 2

Apply log rules

x - 1 = \frac{1}{e ^{2}}

Solve

x - 1 = \frac{1}{e ^{2}} : x = \frac{1}{e ^{2}} + 1

x = \frac{1}{e ^{2}} + 1

Verify Solutions:

x = \frac{1}{e ^{2}} + 1

True

The solution is

x = \frac{1}{e ^{2}} + 1

lo g_{10} (x) = 8.19

0.29 = lo g_{10} (x)

ln (ln (x)) = - 2.8

0.76 = ln (y)

ln (2 x) + 1 = 0