Answer:
x = 1/2
Step by step explanation:
Two numbers a and b are each greater than zero.
i.e a > 0 and b > 0
And;
[tex] \sqrt{a} \: = \: \sqrt[3]{b} [/tex]
Since the square root of a is equal to cube root of b then,
a = b = 1
[tex] {a}^{2x \: - \: 1} \: = \: b[/tex]
[tex] {1}^{2x \: - \: 1} = {1}^{0} [/tex]
2x - 1 = 0
x = 1/2
Two numbers are 'a' and 'b'.
And a > 0, b > 0
[tex]\sqrt{a}=\sqrt[3]{b}[/tex]
[tex]a^{\frac{1}{2} }=b^{\frac{1}{3}}[/tex]
[tex]a=(b)^{\frac{2}{3} }[/tex]
We have to find the value of [tex]x[/tex] if [tex]a^{2x-1}=b[/tex],
By substituting the value of [tex]a[/tex] in the given expression,
[tex](b^{\frac{2}{3}})^{2x-1}=b[/tex]
Now use the laws of exponents,
[tex]b^{\frac{2}{3}(2x-1)}=b[/tex] [Since, [tex](a^m)^n= a^{mn}[/tex]]
By comparing the exponents on both the sides,
[tex]\frac{2}{3}(2x-1)=1[/tex]
[tex]2(2x-1)=3[/tex]
[tex]4x-2=3[/tex]
[tex]4x=5[/tex]
[tex]x=\frac{5}{4}[/tex]
[tex]x=1.25[/tex]
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