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Step-by-step Solution

Solve the equation 3^(2x+1)=3^(8x-3)

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Answer

$x=\frac{2}{3}$

Step-by-step explanation

Problem to solve:

$3^{\left(2x+1\right)}=3^{\left(8x-3\right)}$
1

Removing the variable from the exponent

$\ln\left(3^{\left(2x+1\right)}\right)=\ln\left(3^{\left(8x-3\right)}\right)$
2

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$\ln\left(3\right)\left(2x+1\right)=\ln\left(3^{\left(8x-3\right)}\right)$

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Answer

$x=\frac{2}{3}$
$3^{\left(2x+1\right)}=3^{\left(8x-3\right)}$

Main topic:

Polynomials

Time to solve it:

~ 0.47 seconds