Question

Solve the exponential equation by taking the logarithm on both sides. 5^(x+8)=7

Answer 1

Answer:

x = (log₅7) - 8

Explanation:

Given;

$5^{x+8}$ = 7

Take log of both sides;

log₁₀($5^{x+8}$) = 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) = $\frac{log_{10}7}{log_{10}5}$                -----------(iii)

From the laws of logarithm, remember that;

$\frac{log_{a}x}{log_{a}y} = log_yx$

Equation (iii) can thus be written as;

(x + 8) = log₅7

x + 8 = log₅7

Make x subject of the formula;

x = (log₅7) - 8