Question

Solve for x by using log. Rounded to hundredth. exFormula1" title="10^{4x-5}=e^{3x}" alt="10^{4x-5}=e^{3x}" align="absmiddle" class="latex-formula">

Answer 1

Answer: $x=1.85$

Step-by-step explanation:

 Given the expression $10^{4x-5}=e^{3x}$, apply natural logarithm to both sides. Then:

$ln(10)^{4x-5}=ln(e)^{3x}$

Remember that according the the properties of logarithms:

$ln(a)^m=mln(a)$

$ln(e)=1$

Then:

$(4x-5)ln(10)={3x}$

Apply distributive property and solve for "x". Then you get:

$4x*ln(10)-5ln(10)=3x\\\\4x*ln(10)-3x=5ln(10)\\\\x(4ln(10)-3)=5ln(10)\\\\x=\frac{5ln(10)}{4ln(10)-3}\\\\x=1.85$

Answer 2

Answer:

$x=1.85$

Step-by-step explanation:

The given exponential equation is;

$10^{4x-5}=e^{3x}$

We take logarithm of both sides to base $e$.

$\ln 10^{4x-5}=\ln e^{3x}$

$(4x-5)\ln 10=3x\ln e$

$(4x-5)\ln 10=3x$

Expand the left hand side;

$4x\ln 10-5\ln 10=3x$

Group like terms

$4x\ln 10-3x=5\ln 10$

$(4\ln 10-3)x=5\ln 10$

$x=\frac{5\ln 10}{4\ln 10-3}$

$x=1.85$