What is the inverse of f(x)=log_{10}(3)(4x+5)-6 ?

The inverse of f(x)=log_{10}(3)(4x+5)-6 is (x+6-5log_{10}(3))/(4log_{10)(3)}

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inverse of f(x)=log_{10}(3)(4x+5)-6

inverse

f (x) = lo g_{10} (3) (4 x + 5) - 6

\frac{x + 6 - 5 lo g _{10} ( 3 )}{4 lo g _{10} ( 3 )}

Solution steps

y = lo g_{10} (3) (4 x + 5) - 6

Replace

x

with

y

x = lo g_{10} (3) (4 y + 5) - 6

Solve for

y, x = lo g_{10} (3) (4 y + 5) - 6

\frac{x + 6 - 5 lo g _{10} ( 3 )}{4 lo g _{10} ( 3 )}

f (x) = 3 - 2 x^{2} x - 5

f (x) = 11 - 2 x^{3}

f (x) = - 3 x - 11

f (x) = \frac{x}{5} + 8

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

What is the inverse of f(x)=log_{10}(3)(4x+5)-6 ?
The inverse of f(x)=log_{10}(3)(4x+5)-6 is (x+6-5log_{10}(3))/(4log_{10)(3)}