What is the answer to log_{10}(9^x)=1.5 ?

The answer to log_{10}(9^x)=1.5 is x=(1.5ln(10))/(2ln(3))

Solve for x: log_{10}(9^x)=1.5

The solution is x=(1.5ln(10))/(2ln(3))

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lo g_{10} (9^{x}) = 1.5

x = \frac{1.5 ln ( 10 )}{2 ln ( 3 )}

Decimal Notation

x = 1.57192 \dots

Solution steps

lo g_{10} (9^{x}) = 1.5

Rewrite the equation with

9^{x} = u

lo g_{10} (u) = 1.5

Solve

lo g_{10} (u) = 1.5 : u = 1 0^{1.5}

u = 1 0^{1.5}

Substitute back

u = 9^{x},

solve for

x

Solve

9^{x} = 1 0^{1.5} : x = \frac{1.5 ln ( 10 )}{2 ln ( 3 )}

x = \frac{1.5 ln ( 10 )}{2 ln ( 3 )}

1 0^{x} = 33

3^{x} + 2 x - 5 = 0

2^{5 x + 2} = 8^{9}

(\frac{( 2 ^{1 - 2 x} )}{( 2 ^{x + 3} )})^{3} = 4

y, \frac{( 2 ^{y} - 1 )}{( 2 ^{y} + 1 )} = x

What is the answer to log_{10}(9^x)=1.5 ?
The answer to log_{10}(9^x)=1.5 is x=(1.5ln(10))/(2ln(3))
Solve for x: log_{10}(9^x)=1.5
The solution is x=(1.5ln(10))/(2ln(3))