What is the answer to solvefor a,x^{a+b}=x^a+x^b ?

The answer to solvefor a,x^{a+b}=x^a+x^b is a=(bln(x)-ln(x^b-1))/(ln(x))

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solvefor a,x^{a+b}=x^a+x^b

solve for

a, x^{a + b} = x^{a} + x^{b}

a = \frac{b ln ( x ) - ln ( x ^{b} - 1 )}{ln ( x )}

Solution steps

x^{a + b} = x^{a} + x^{b}

Subtract

x^{a}

from both sides

x^{a + b} - x^{a} = x^{a} + x^{b} - x^{a}

Simplify

x^{a + b} - x^{a} = x^{b}

Factor

x^{a + b} - x^{a} : x^{a} (x^{b} - 1)

x^{a} (x^{b} - 1) = x^{b}

Divide both sides by

x^{b} - 1

x^{a} = \frac{x ^{b}}{x ^{b} - 1}

Apply exponent rules

a ln (x) = ln (\frac{x ^{b}}{x ^{b} - 1})

Solve

a ln (x) = ln (\frac{x ^{b}}{x ^{b} - 1}) : a = \frac{b ln ( x ) - ln ( x ^{b} - 1 )}{ln ( x )}

a = \frac{b ln ( x ) - ln ( x ^{b} - 1 )}{ln ( x )}

4 (4^{2 x}) - 17 (4^{x}) + 4 = 0

2^{2 x + 3} - 8 \cdot 2^{x + 1} + 8 = 0

2^{2 x - 5} = 8

7^{10} = 7^{5} \cdot 7^{f}

2^{x} - 5 = 59

What is the answer to solvefor a,x^{a+b}=x^a+x^b ?
The answer to solvefor a,x^{a+b}=x^a+x^b is a=(bln(x)-ln(x^b-1))/(ln(x))