What is the answer to log_{3}(7^{5x})=10 ?

The answer to log_{3}(7^{5x})=10 is x=(2ln(3))/(ln(7))

Solve for x: log_{3}(7^{5x})=10

The solution is x=(2ln(3))/(ln(7))

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lo g_{3} (7^{5 x}) = 10

x = \frac{2 ln ( 3 )}{ln ( 7 )}

Decimal Notation

x = 1.12915 \dots

Solution steps

lo g_{3} (7^{5 x}) = 10

Rewrite the equation with

7^{5 x} = u

lo g_{3} (u) = 10

Solve

lo g_{3} (u) = 10 : u = 59049

u = 59049

Substitute back

u = 7^{5 x},

solve for

x

Solve

7^{5 x} = 59049 : x = \frac{2 ln ( 3 )}{ln ( 7 )}

x = \frac{2 ln ( 3 )}{ln ( 7 )}

3^{x} = e^{x}

(3^{4})^{2} = 3^{p}

243 = 3^{x}

(\frac{1}{4})^{x} = 8

What is the answer to log_{3}(7^{5x})=10 ?
The answer to log_{3}(7^{5x})=10 is x=(2ln(3))/(ln(7))
Solve for x: log_{3}(7^{5x})=10
The solution is x=(2ln(3))/(ln(7))