What is the answer to 5*10^{z/4}=32 ?

The answer to 5*10^{z/4}=32 is z=(4ln(32/5))/(ln(10))

Solve for z: 5*10^{z/4}=32

The solution is z=(4ln(32/5))/(ln(10))

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5 \cdot 1 0^{\frac{z}{4}} = 32

z = \frac{4 ln ( \frac{32}{5} )}{ln ( 10 )}

Solution steps

5 \cdot 1 0^{\frac{z}{4}} = 32

Divide both sides by

5

1 0^{\frac{z}{4}} = \frac{32}{5}

Apply exponent rules

\frac{z}{4} ln (10) = ln (\frac{32}{5})

Solve

\frac{z}{4} ln (10) = ln (\frac{32}{5}) : z = \frac{4 ln ( \frac{32}{5} )}{ln ( 10 )}

z = \frac{4 ln ( \frac{32}{5} )}{ln ( 10 )}

3^{2 x + 1} + 3 = 10 \cdot 3^{x}

e^{3 x + 1} = 100

5 = 6^{x}

ln (e^{x}) = 1

2 e^{3 x} = 4 e^{5 x}

What is the answer to 5*10^{z/4}=32 ?
The answer to 5*10^{z/4}=32 is z=(4ln(32/5))/(ln(10))
Solve for z: 5*10^{z/4}=32
The solution is z=(4ln(32/5))/(ln(10))