Answer:
x = (log₅7) - 8
Explanation:
Given;
[tex]5^{x+8}[/tex] = 7
Take log of both sides;
log₁₀([tex]5^{x+8}[/tex]) = log₁₀7 -------------(ii)
From the laws of logarithm remember that;
logₐ xⁿ = n logₐ x
Equation (ii) can then be written as;
(x + 8)log₁₀5 = log₁₀7
Divide both sides by log₁₀5
(x + 8) = [tex]\frac{log_{10}7}{log_{10}5}[/tex] -----------(iii)
From the laws of logarithm, remember that;
[tex]\frac{log_{a}x}{log_{a}y} = log_yx[/tex]
Equation (iii) can thus be written as;
(x + 8) = log₅7
x + 8 = log₅7
Make x subject of the formula;
x = (log₅7) - 8
