What is the answer to 5^x-1+5^x-2=30 ?

The answer to 5^x-1+5^x-2=30 is x=(ln(33/2))/(ln(5))

Solve for x: 5^x-1+5^x-2=30

The solution is x=(ln(33/2))/(ln(5))

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5^{x} - 1 + 5^{x} - 2 = 30

x = \frac{ln ( \frac{33}{2} )}{ln ( 5 )}

Decimal Notation

x = 1.74182 \dots

Solution steps

5^{x} - 1 + 5^{x} - 2 = 30

Group like terms

5^{x} + 5^{x} - 1 - 2 = 30

Add similar elements:

5^{x} + 5^{x} = 2 \cdot 5^{x}

2 \cdot 5^{x} - 1 - 2 = 30

Subtract the numbers:

- 1 - 2 = - 3

2 \cdot 5^{x} - 3 = 30

Move

3

to the right side

2 \cdot 5^{x} = 33

Divide both sides by

2

5^{x} = \frac{33}{2}

Apply exponent rules

x ln (5) = ln (\frac{33}{2})

Solve

x ln (5) = ln (\frac{33}{2}) : x = \frac{ln ( \frac{33}{2} )}{ln ( 5 )}

x = \frac{ln ( \frac{33}{2} )}{ln ( 5 )}

2^{x} = 0.25

(3^{42} \cdot 9^{12})^{\frac{1}{3}} = 3^{k}

x, 2^{2 y + 4} = 1 6^{x}

1 0^{x} + 1 0^{- x} = 4

(d^{2} - 9) = (e^{3})^{x} + e^{- 3} x

What is the answer to 5^x-1+5^x-2=30 ?
The answer to 5^x-1+5^x-2=30 is x=(ln(33/2))/(ln(5))
Solve for x: 5^x-1+5^x-2=30
The solution is x=(ln(33/2))/(ln(5))