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Solve for [tex]\( x \)[/tex]:

[tex]\[ 7^{2x} = 49 \][/tex]


Sagot :

To solve the equation [tex]\(7^{2x} = 49\)[/tex]:

1. Express 49 as a power of 7: Notice that 49 can be written as [tex]\(7^2\)[/tex].
[tex]\[ 49 = 7^2 \][/tex]

2. Substitute [tex]\(7^2\)[/tex] into the equation: Replace 49 in the given equation with [tex]\(7^2\)[/tex].
[tex]\[ 7^{2x} = 7^2 \][/tex]

3. Set the exponents equal to each other: Since the bases (7) are the same, we can equate the exponents.
[tex]\[ 2x = 2 \][/tex]

4. Solve for [tex]\(x\)[/tex]: Divide both sides of the equation by 2.
[tex]\[ x = \frac{2}{2} = 1 \][/tex]

So, the solution to the equation [tex]\(7^{2x} = 49\)[/tex] is [tex]\(x = 1\)[/tex].