What is the answer to 5^r+1=51 ?

The answer to 5^r+1=51 is r=(ln(50))/(ln(5))

Solve for r: 5^r+1=51

The solution is r=(ln(50))/(ln(5))

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5^{r} + 1 = 51

r = \frac{ln ( 50 )}{ln ( 5 )}

Decimal Notation

r = 2.43067 \dots

Solution steps

5^{r} + 1 = 51

Move

1

to the right side

5^{r} = 50

Apply exponent rules

r ln (5) = ln (50)

Solve

r ln (5) = ln (50) : r = \frac{ln ( 50 )}{ln ( 5 )}

r = \frac{ln ( 50 )}{ln ( 5 )}

k, 4^{k} = n^{2}

2 \times 3^{x - 2} = 162

e^{x^{2} + 3} = e^{4 x}

85 \cdot 3^{x} = 765