What is the answer to log_{7}(2^{5x})=3 ?

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

Solve for x: log_{7}(2^{5x})=3

The solution is x=(3ln(7))/(5ln(2))

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lo g_{7} (2^{5 x}) = 3

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

Decimal Notation

x = 1.68441 \dots

Solution steps

lo g_{7} (2^{5 x}) = 3

Rewrite the equation with

2^{5 x} = u

lo g_{7} (u) = 3

Solve

lo g_{7} (u) = 3 : u = 343

u = 343

Substitute back

u = 2^{5 x},

solve for

x

Solve

2^{5 x} = 343 : x = \frac{3 ln ( 7 )}{5 ln ( 2 )}

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

7^{x - 5} = 4 9^{x}

8 1^{\frac{x}{4}} = \frac{1}{37}

5000000 = 1000000 e^{0.645 (t)}

2^{2 x} - 9 (2^{x}) + 8 = 0

5^{x} = \frac{5 ^{x}}{625}

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