What is the answer to log_{7}(x)=log_{7}(a)*b^2-log_{7}(a^3*b) ?

The answer to log_{7}(x)=log_{7}(a)*b^2-log_{7}(a^3*b) is x=(a^{b^2-3})/b

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log_{7}(x)=log_{7}(a)b^2-log_{7}(a^3b)

lo g_{7} (x) = lo g_{7} (a) \cdot b^{2} - lo g_{7} (a^{3} \cdot b)

x = \frac{a ^{b^{2} - 3}}{b}

Solution steps

lo g_{7} (x) = lo g_{7} (a) b^{2} - lo g_{7} (a^{3} b)

Apply log rules

x = \frac{a ^{b^{2} - 3}}{b}

- 4 = 20 \cdot lo g_{10} (\frac{x}{80})

ln (x^{2} + 6) - ln (x - 2) = ln (x + 1)

lo g_{10} (n) = 1.0043

lo g_{10} (x) + lo g_{10} (7) = lo g_{10} (4)

lo g_{\frac{1}{2}} (x^{2} - 3) = lo g_{2} (x^{2})

What is the answer to log_{7}(x)=log_{7}(a)*b^2-log_{7}(a^3*b) ?
The answer to log_{7}(x)=log_{7}(a)*b^2-log_{7}(a^3*b) is x=(a^{b^2-3})/b